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{\bf CURRICULUM VITAE OF DORON ZEILBERGER}
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{\bf Last Update: Nov. 16, 2007}
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{\bf Address}
\medskip
Doron Zeilberger, Department of Mathematics,
Hill Center-Busch Campus, Rutgers University
110 Frelinghuysen Rd Piscataway, NJ 08854-8019
(732) 445-1326. zeilberg@math.rutgers.edu  .
\medskip
Home Page: http://www.math.rutgers.edu/\Tilde zeilberg/
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{\bf Personal Data}
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Date of Birth:    July 2, 1950.
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Place of Birth:   Haifa, Israel.
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Marital Status:   Married (Jane Legrange), three children (Celia, 
Tamar, Hadas).
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Citizenship: USA (naturalized Jan 1988.)
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{\bf Education}
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University of London, B.Sc. with First Class Honours, 1972.
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The Weizmann Institute of Science, Israel, Ph.D., 1976.
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{\bf Employment History}
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2001- : Rutgers University (New Brunswick), Board of Governors Professor.
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2000-2001: Temple University, Laura H. Carnell Professor.
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1990- 1999:  Temple University, Professor.
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1988-1990:  Drexel University, Professor. 
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1983-1988:  Drexel University, Associate Professor.
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1982-1983:  University of Pennsylvania, Lecturer.
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1980-1982:  The Weizmann Institute of Science, Senior Scientist.
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1979-1980:  University of Illinois, Urbana, Visiting Lecturer.
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1978-1979:  Georgia Institute of Technology, Visiting Assistant
Professor.
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1977-1978 and Fall 1993:  Institute for Advanced Study, Princeton, Member.
\medskip
{\bf Current Research Interests}
\medskip
Experimental Mathematics,
Computer Algebra, Combinatorics and Special Functions.
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{\bf Prizes}
\medskip
1) 1983-With David Bressoud won \$50 from Richard Askey and George
Andrews for the proof of the q-Dyson conjecture.
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2) 1985-Won 10 bottles of wine from G. Xavier Viennot for a bijection
between binary trees with n leaves and Strahler number k and
ordered trees with n vertices and pruning order k.
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3) 1986-With Laurent Habsieger won \$50 from Richard Askey for
a proof of the $G_2$ case of Macdonald's root system conjecture.
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4) 1987- Won \$50 from Richard Askey for a proof of the $G_2$- dual 
case of the Macdonald-Morris conjecture.
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5) 1990- The Lester R. Ford award for ``the best paper in the
American Mathematical Monthly in 1989". Given for my paper
``Kathy O'Hara's constructive proof of the unimodality of the
Gaussian polynomials". (Monetary Award: \$500). Reference:
{\it Notices of the AMS} {\bf37}, \#8 (Oct 1990), p. 1034;
{\it Focus} {\bf10} \#6 (Nov-Dec 1990) p. 9.
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6) 1998-The AMS Leroy Steele prize for `seminal contributions to
research', joint with Herb Wilf. (Monetary award: (1/2)(\$4000)).
Reference:{\it Notices of the AMS} {\bf 45}, \#4 (Apr. 1998), pp. 504-508;
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7) 1998-With Aaron Robertson (jointly)
and Tomasz Schoen (independently) won \$100 from Ron Graham for
a determining the asymptotic minimal number of Schur triples.
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8) 2004-Euler Medal for ``outstanding contributions to combinatorics'',
Institute of Combinatorics and Its Applications.
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{\bf Invited, Plenary, and Keynote Conference Talks}
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May 1982 - Oberwolfach.
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May 1985 - Arizona State Andrews Conference.
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June 1985 - Colloque de Combinatoire Enumerative, UQAM, Montreal.
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December 1986 - Gillis Symposium, Rehovot, Israel.
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March 1988-Workshop on q-series, Institute of Mathematics and its
applications, Minnesota.
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July 1988 - Oberwolfach.
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June 1989 - Joint AMS SIAM meeting on Probabilistic and Analytical
Methods in Combinatorics, Arcata, Ca.
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May 1990 - S\'eminaire Lotharingien  de combinatoire, Alsace (Principal
Speaker).
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December 1990 - Special Session on algebraic combinatorics, Canadian
Mathematical Society Annual Conference, Waterloo, Ontario.
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May 1991 - Formal Power Series and Algebraic Combinatorics III,
Bordeaux, France.
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July 1991 - Minisymposium on constructive combinatorics, ICIAM,
Washington, DC.
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March 1993 - Special session in combinatorics, AMS Meeting,
Knoxville, TN.
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May 1993 - JERUSALEM Combinatorics 
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September 1993 - Workshop on ``combinatorics and computer algebra",
Cornell University, Ithaca, NY. (Principal speaker)
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May 1994 - Algebraic Combinatorics III, Ann Arbor, MI.
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Nov 1994 - AMS, Richmond, VA. (Hour Speaker.)
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Jan. 1995 - Oberwolfach
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June 1995 - Principal Lecturer, Fields Institute
workshop on Special Functions, on `special functions and computer algebra.
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Jan. 1996 - Oberwolfach
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June 1996 - Wilf symposium
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July 1996 - SOCA 96', Nankagi Inst., Tijanin, China.
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Oct. 1996 - MSRI, Berkely, Workshop on Enumeration and Posets.
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May 1997 - Workshop on experimental mathematics and combinatorics., CRM,
Montreal.
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Aug. 1997 - Number Theory and Combinatorics, Penn State, (plenary).
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June 1998 - AMS Summer conference on special functions, q-series, and
combinatorics, Mt. Holyoke.
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July 1998 - IWOP 4, Madrid, Spain , (plenary).
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Aug. 1998 - Combinatorics and Physics, Los Alamos.
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Oct. 1998 - MSRI workshop on computer algebra (plenary).
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Nov. 1998 - EPADEL MAA sectional meeting (plenary).
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Nov. 1999 - Symbolic Computation, Combinatorics, and Physics,
Gainseville (plenary).
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Sept. 2000 - LACIM 2000, Montr\'eal .
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March 2001 - Frontiers of Mathematics Lecturer (3 talks), Texas A\&M
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March 2001 - CombinaTexas
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April 2001 - MAA NJ Section (plenary).
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June 2001 - IJCAR, Siena, Italy (plenary).
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Aug. 2001 - ICDEA, Augsburg, Germany
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May 2002 - ECCAD 2002, Queens, NY (plenary).
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July 2002 - IMA Workshop on Special Functions for the Digital age, Minneapolis.
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Aug. 2002 - International Congress on Mathematical Software 2002, Beijing 
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Sept. 2002 - DMSCSD 2002, Albany (plenary)
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Oct. 2002 - Bruno Buchberger's 60th Birthday Conference, RISC-Linz (plenary).
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April 2003 - Joyal Symposium, LACIM, Montreal.
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May 2003 - Zeilberger MiniConference, MIT, Cambridge, MA.
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June 2003 - ``Alternating Sign Matrices Conference'', in honor
of David Robbins, IDA-CCR, Princeton, NJ.
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Oct. 2003 - Howard-Hayden Lecturer, Univ. of Kentucky.
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Sept. 2004 - ADG2004, Gainseville, keynote .
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March 2005 - 3rd conference on Pattern Avoidance, (keynote )
\medskip
March 2005 - Special year in Combinatorics and Number Theory, 
Gainseville, History Lecture
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July 2005- Mathematics and Narrative, Mykonos, Greece.
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March 2006- 37th International Southeastern Conference on
Combinatorics, Graph Theory, and Computing, Boca Raton, Florida (plenary).
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April 2006-Waterloo Workshop on Computer Algebra, in honor of S.A. Abramov.
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April 2006- Graduate Student Combinatorics Conference, Madison, Wisconsin
(keynote).
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Oct. 2006-``Enumerative Combinatorics'', Harvey Mudd College, Claremont, CA
(plenary)
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Jan. 2007- Special Session on Experimental Mathematics, AMS Annual
Meeting, New Orleans, LA. 
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 Feb. 2007-``Distinguished Lecture Series'' (Feb. 20, 2007)
Math. Assoc. America, Washington, DC.
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Feb. 2007-``Combinatorial Problems Raised by Statistical
Mechanics'', Univ. of Montr\'eal. (plenary)
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Oct. 2007- Center For Communication Research [Inst. for Defense Analyses]
 (internal) conference,
Princeton, NJ. (keynote)
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Nov. 2007-  Symposium to Celebrate Gregory Chaitin's 60th Birthday,
IBM Watson Research, Yorktown  Heights, NY
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Jan. 2008- Special Session on Applications of Computer
Algebra to Combinatorics, AMS Annual
Meeting, San Diego, CA.
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April 2008 - MAA NJ Section (plenary).
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May 2008-Waterloo Workshop on Computer Algebra, in honor of 
Gregory Egorychev's 70th Birthday.
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Dec. 2009-Austo-Asian Combinatorics Conference, New Zealnd.

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{\bf Further Information:}
\medskip
1) Held  one month visiting professorships, University of Strasbourg,
March 1983, May 1990, July 1994.
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2) Invited speaker in the special years in Combinatorics, MIT, 1984-1985;
Mittag-Leffler Inst., Sweden, 1991-92.
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3) Erd\"os Number:2 (via J.Gillis).
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4) Considered an outstanding teacher.
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5) Co-editor (with P. Paule) of special issue of J. Symbolic Computation
on ``combinatorics and computer algebra", 1992.
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6) Member of Program Committee, Formal Power Series and 
Algebraic Combinatorics IV, (June 92, Montr\'eal), and V (June 93,
Florence), and VI (June 94, Rutgers).
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7) ``Bourbakis\'e" (Expose 746, by P. Cartier,  appeared in the
1991-92 volume of the S\'eminaire Bourbaki, Ast\'erisque {\bf 206}.)
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8) Member of International Advisory Committee of the  Special Functions
workshop to be held at the Fields Inst., June, 1995.
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9) Member of Scientific Committee for special year on ``Combinatorics
and Theory of Groups'', CRM, Montreal, 1996-1997.
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10) ``Gosper's and Zeilberger's Algorithms" is subject classification
33F10 of Math Reviews.
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11) Chosen by Persi Diaconis as ``favorite (still living!) mathematician''.


\bigskip

{\bf Grants and Contracts:}
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NSF DMS-8400204: ``Proving Identities by Combinatorial Methods"
(1984-1986), Principal Investigator, \$24,000.
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NSF DMS-8600243: ``Towards a General Theory of Combinatorial Bijections"
(1986-1988), Principal Investigator, \$36,000.
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NSF DMS-8800663:``Constant Term Identities and Combinatorial Enumeration"
(1988-1991), Principal Investigator. \$60,000.
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NSF DMS-8901610:``Asymptotic Methods in Combinatorics" (1989-1992),
co-Principal Investigator (joint with Prof. Jet Wimp, Drexel University).
\$120,00.
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NSF DMS-9123836:``Computer-Generated and Computer-Assisted research in
Combinatorics and Special Functions, (1992-1995) Principal
Investigator, \$180,000.
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NSF DMS-9500646:``Combinatorics, Special Functions, 
and Computer Algebra''(1995-1998),
 Principal Investigator, \$120,000.
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NSF DMS-9732602:``Targeted Proofs Machines in Combinatorics''
(1998-2001), Principal Investigator, \$180,000.
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NSF DMS-9732602:``Targeted Proofs Machines in Combinatorics''
(1998-2001), Principal Investigator, \$180,000.
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NSF DMS-00403:``Symbolic Computation and Combinatorics''
(2001-2004), Principal Investigator, \$180,000.
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NSF DMS-0401124:``Automating Combinatorics''
(2004-2009), Principal Investigator, \$175,000 (plus two \$18000 supplements
so far, and one pending).

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{\bf Service to the Profession:}
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{\bf Co-Editor in Chief} of {\it Advances in Applied Mathematics}.
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{\bf Member of Editorial Boards of}: J. of Difference Eq. and Applications,
Electronic J. of Combinatorics, 
Ramanujan Quarterly, Annals of Combinatorics, INTEGERS,
J. of Symbolic Computation.

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{\bf Ph.D. Theses Supervised:}
\smallskip                                      
Sheldon Parnes, Temple, 1993, [Industry, Coloardo].
\smallskip                                      
Ethan Lewis, Penn, 1994, [IBM, Israel].
\smallskip                                      
Craig Orr, Temple, 1994, [National Security Agency].
\smallskip                                      
John Majewicz, Temple, 1997, [Comm. College of Phila].
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John Noonan, Temple, 1997, [Mt. Vernon Nazarene College, OH].
\smallskip                                      
Tewodros Amdeberhan, Temple, 1997, [currently visiting professor at Tulane University].
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Melkamu Zeleke, Temple, 1998, [Wiiliam Patterson Univ., Wayne, NJ].
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Aaron Robertson, Temple, 1999, [Colgate Univ., Hamilton, NY].
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Akalu Tefara, Temple, 2000, [Grand Valley State Univ., MI, currently visiting Assoc. Prof. MIT].
\smallskip                                      
Anne Edlin, Temple, 2000, [Lasalle University, PA]
\smallskip                                      
Xinyu Sun, Temple, 2004, [Texas A\&M]
\smallskip                                      
Xiadong Wen, Temple, 2005 [Wolfram Research]
\smallskip                                      
Vince Vatter, Rutgers, 2005 [St. Andrews Univ., Scotland, then D.E. Shaw, going to Darthmouth]
\smallskip                                      
Moa Apagodu, Rutgers, 2006 [Virginia Commonwealth University]
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{\bf Current Ph.D. Students:}
\smallskip                                      
Andrew Baxter,
Arvind Ayyer [joint with Joel Lebowitz],
Emilie Hogan,
Lara Pudwell, Eric Rowland, Thotsaporn Thanatipanonda.

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{\bf Co-Chair of Organizing Committee:} `Classical Combinatorics',
an International Conference in honor of Dominique Foata, July 7-10, 2000.

\bigskip 
{\bf Past Courses Taught:}
\medskip
{\bf Calculus:}
1982-1983 (Penn), 1983-1990 (Drexel), 1990-2000 (Temple):
Number of students ranging
from 12 (Honours) to 250 (large lecture). Whenever there is
a common final, my sections, score, on the average, 
between 10 to 20 points (out of 100) higher than the average section.
I was the only professor at Penn (1982-1983) who made it to the
list of ``best teachers" in all his four courses.
Calculus I (Fall 2003), 
Calculus I (Fall 2004), Calculus II (Fall 2005).

\bigskip
{\bf Other Past Undergraduate Courses:} Linear Algebra, Differential Equations,
Advanced Calculus for Engineering,
Mathematical Programming, Computer Algebra, Problem-Solving.
Multivariate Calculus, Graph Theory..

\bigskip
{\bf Past Graduate Courses:} Computer Algebra and Experimental Mathematics
(1990, 1992, 1994, 1996, 1998, 1999).
Combinatorics (1991, 1993, 1995, 1997, 2000, 2001, 2003, 2004).
Famous Open Problems (1999).
Experimental Mathematics (Fall 2001, 2003-2007), Probability (Spring 2002),
Combinatorics I and II(Fall 2002 and Spring 2003 respectively).
Discrete Algorithms (Spring 2005), 

\bigskip
{\bf Current  Course (Spring 2008)}

Experimental Mathematical via Enumerative Combinatorics.

{\bf Software Development} 

My website
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/} has many
computer-algebra packages available free of charge. They are used
not only by mathematicians, but also by scientists, especially
physicists, computer-scientists, and engineers, who need
combinatorial sums and special functions on a regular basis.
My algorithms are now part of {\tt Maple } (the packages
{\tt sumtools} and {\tt SumTools}), 
and soon will also be part of Mathematica.
 
\bigskip
{\bf Curriculum  Development} 

An innovative  grad course in Experimental Math is currently
under development, that will hopefully turn into the
first textbook in this new area.

\bigskip
{\bf Seminar Organizer}

With graduate students Andrew Baxter and
Lara Pudwell, I am organizing a very successful and
innovative seminar on Experimental Mathematics.
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\bigskip
 
\centerline{\bf PUBLICATIONS}
\medskip
 
This list, as well as most of the papers published after 1990, are available 
at

{\tt http://www.math.rutgers.edu/\Tilde zeilberg}.

1. (With D. Nicholson, P. Rabinowitz and N. Richter) {\it On the Error in
the Numerical Integration of Chebyshev Polynomials}, Math.
Computation {\bf 25}, 79-86 (1971).
 
2. {\it Uniqueness Theorems for Harmonic Functions of Exponential
Growth}, Proc. Amer. Math. Soc. {\bf 61},  335-340 (1976).
 
3. {\it Binary Operations in the set of solutions of a Partial
Difference Equation}, Proc. Amer. Math. Soc. {\bf 62}, 242-244
(1977).
 
 
4. {\it A new approach to the theory of Discrete Analytic
Functions}, J. Math. Anal. Appl. {\bf 57}, 350-367 (1977).
 
 
5. (With H.Dym) {\it Further properties of Discrete Analytic
Functions}, J. Math. Anal. Appl. {\bf 58}, 405-418 (1977).
 
 
6. {\it A new basis for Discrete Analytic Functions}, J. Australian
Math. Soc. {\bf 23} (series A), 95-104 (1977).
 
 
7. {\it Discrete Analytic Functions of exponential growth}, Trans.
Amer. Math. Soc. {\bf 226}, 181-189 (1977).
 
 
8. {\it A discrete analog of the Paley-Wiener theorem in a half
plane}, J. Australian Math. Soc. (Series A) {\bf 23},
376-378 (1978).
 
 
9. {\it A new proof of Ehrenpreis's semi-local Quotient Structure
Theorem}, Amer. J. Math. {\bf 100}, 1317-1332 (1978).
 
 
10. {\it The Pompeiu problem for discrete space}, Proc. Natl. Acad.
Sci. {\bf 75}, 3555-3556 (1978).
 
 
11. {\it  Solutions of exponential growth to systems of partial
differential equations}, J. Diff. Eq. {\bf 31}, 287-295 (1979).
 
 
12. {\it  The algebra of linear partial difference operators and its
applications}, SIAM J. Math. Anal. {\bf 11}, 919-934 (1980).
 
 
13. {\it  Some comments on Rota's umbral calculus}, J. Math. Anal.
Appl. {\bf 74}, 456-463 (1980).
 
 
14. {\it  A lattice walk approach to the q-counting of multiset
permutations}, J. Math. Anal. Appl. {\bf 74}, 192-199 (1980).
 
 
15. {\it  Partial difference equations in $ m_1 \geq ... \geq m_n
\geq 0 $ and their applications to combinatorics}, Discrete Math
{\bf 31}, 65-77 (1980).
 
 
16. {\it  Enumerating words by their number of mistakes}, Discrete
Math {\bf 34}, 89-91 (1981).
 
 
17. {\it  All binomial identities are verifiable}, Proc. Natl. Acad.
Sci. {\bf 78}, 4000 (1981).
 
 
18. {\it  Sister Celine's technique and its generalizations}, J. Math.
Anal. Appl. {\bf 85}, 114-145 (1982).
 
 
19. (With D. Franzblau) {\it  A bijection proof of the hook length
formula}, J. Algorithms {\bf 3}, 317-343 (1982).
 
 
20. (With D. Bressoud) {\it A short Rogers-Ramanujan bijection},
Discrete Math. {\bf 38}, 313-315 (1982).
 
 
21. {\it  A combinatorial proof of Dyson's conjecture}, Discrete
Math. {\bf 41}, 317-321 (1982).
 
 
22. (With S. R. Caplan) {\it T. L. Hill's graphical method for solving
linear equations}, Advances in Appl. Math. {\bf 3}, 377-383
(1982).
 
 
23. (With L. Shapiro) {\it A Markov chain occurring in Enzyme
Kinetics}, J. Math. Biology {\bf 15}, 351-357 (1982).
 
 
24. (With J. Gillis) {\it A direct combinatorial proof of a positivity
result}, European J. Comb. {\bf 4}, 221-223 (1983).
 
 
25. {\it  Andre's reflection proof generalized to the many-candidate
ballot problem}, Discrete Math {\bf 44}, 325-326 (1983). 
 
 
26. (With J. Gillis and B. Reznick) {\it  Elementary methods in positivity
theory}, SIAM J. Math. Anal. {\bf 14}, 396-398 (1983).
 
 
27. {\it A combinatorial proof of Newton's identities}, Discrete
Math. {\bf 49}, 319 (1984).
 
 
28. {\it  A short hook-length bijection inspired by the
Greene-Nijenhuis-Wilf proof}, Discrete Math. {\bf 51}, 101-108 
(1984).
 
 
29. {\it  Garsia and Milne's proof of the inclusion-exclusion
principle}, Discrete Math. {\bf 51}, 109-110 (1984).
 
 
30. (With D. Foata) {\it Weighted derangements and Laguerre
polynomials}, Actes S\'emin. Lotharingien 
de combinatoire {\bf 8}, 20-29 (1984).
 
 
31. (With E. A. Bender) {\it Some asymptotic bijections}, J. Comb. Th.
(Ser A) {\bf 38}, 96-98 (1985).
 
 
32. (With D. Bressoud) {\it A proof of Andrews' q-Dyson conjecture},
Discrete Math. {\bf 54}, 201-224 (1985).
 
 
33. (With J. Wimp) {\it Resurrecting the asymptotics of linear
recurrences}, J. Math. Anal. Appl. {\bf 111}, 162-177 (1985).
 
 
34. {\it  A combinatorial approach to matrix algebra}, Discrete
Math. {\bf 56}, 61-72 (1985).
 
 
35. (With D. Bressoud) {\it Bijecting Euler's partitions recurrence},
Amer. Math. Monthly {\bf 92}, 55-56 (1985).
 
 
36. (With M. Werman) {\it Bijecting Cassini's Fibonacci identity},
Discrete Math. {\bf 58}, 109 (1986).
 
 
37. {\it  Toward a combinatorial proof of the Jacobian conjecture?},
Proc. of the "Colloque de combinatoire \'enum\'erative", G.Labelle and
P.Leroux, editors, Lecture Notes in Math. {\bf 1234}, 370-380,
Springer-Verlag, Berlin (1987). 
 
 
38. {\it A proof of the $ G_2 $ case of Macdonald's root
system-Dyson conjecture}, SIAM J. Math.
Anal. {\bf 18}, 880-883 (1987).
 
 
39. (With D. Bressoud) {\it Generalized Rogers-Ramanujan identities}, 
Advances in Math. {\bf78}, 42-75 (1989).
 
 
40. {\it  A q-Foata proof of the q-Saalsch\"utz identity},  European
J. Comb. {\bf 8}, 461-463 (1987).
 
 
41. {\it Enumerating totally clean words}, Discrete
Math. {\bf 64}, 313-315 (1987).
 
 
42. {\it One line proofs of the unimodality of The Gaussian
polynomials $G(n,k)$, for $k=3,4$}, Ars Comb.,  {\bf 24}, 165-166 (1987).
 
 
43. {\it A bijection from ordered trees to binary trees that sends the
pruning order to the Strahler number}, Discrete Math. {\bf 82},
89-92 (1990).
 
 
44. (With J. Gillis and J. Jedwab) {\it  A combinatorial interpretation of
the integral of the products of Legendre polynomials},  SIAM J.
Math. Anal. {\bf 19}, 1455-1461 (1988).
 
 
45. {\it A unified approach to Macdonald's root-system conjectures},
SIAM J. Math. Anal. {\bf 19}, 987-1013 (1988).
 
 
46. {\it A Stembridge-Stanton style proof of the Habsieger-Kadell
q-Morris identity}, Discrete Math. {\bf 79}, 313-322 (1989/90).
 
 
47. (With D. Foata) {\it Laguerre polynomials, weighted derangements,
and positivity}, SIAM J. Discrete Math. {\bf 1}, 425-433 (1988).
 
 
48. (With D. Foata) {\it Linearization coefficients for the Jacobi
polynomials}, Actes S\'eminaire Lotharingien {\bf 16}, 73-86, Publ.
I.R.M.A., Strasburg (1988).
 
 
49. {\it Six Etudes in generating functions}, Intern. J. Computer
Math. {\bf 29}, 201-215 (1989).
 
 
50. {\it  A combinatorial problem that arose in biophysics}, Fibonacci
Quarterly {\bf 27}, 372 (1989).
 
 
51. {\it  On a conjecture of R.J.Simpson about exact covering
sequences}, Amer. Math. Monthly {\bf 96}, 243 (1989).
 
 
52. {\it  Kathy O'hara's constructive proof of the unimodality of the
Gaussian polynomials}, Amer. Math. Monthly {\bf 96},
590-602 (1989).
 
 
53. {\it  One line proofs of the unimodality of the Gaussian polynomials
$G(n,k)$ for $k < 20$}, in: D. Stanton, 
ed., ``q-Series and Partitions", 
(Proc., IMA, March 1988), IMA series {\bf 18}, Springer, 35-44 (1989).
 
 
54. (With D. Stanton) {\it The Odlyzko conjecture and O'Hara's
unimodality proof}, Proc. Amer. Math. Soc. {\bf 107}, 39-42
(1989).
 
 
55. {\it  Identities}, in: D. Stanton, ed., ``q-Series and Partitions",
(Proc., IMA, March 1988), IMA series {\bf 18}, 67-75 (1989).
 
 
56. {\it A Holonomic systems approach to special functions
identities}, J. of Computational and Applied Math. {\bf 32},
321-368 (1990).
 
 
57. (With S. B. Ekhad) {\it A $21^{st}$ century proof of
Dougall's hypergeometric identity}, J. Math. Anal. Appl. {\bf 147},
610-611 (1990).
 
 
58. {\it  A Fast Algorithm for proving terminating hypergeometric
identities}, Discrete Math {\bf 80}, 207-211, (1990).
 
 
59. (With H. S. Wilf) {\it Rational functions certify combinatorial
identities}, J. Amer. Math. Soc. {\bf 3}, 147-158 (1990).
 
 
60. (With J. Wimp) {\it How likely is Polya's drunkard to stay in  $x \geq
y \geq z$ ?}, J. Statistical Physics {\bf 57}, 1129-1135 (1989).
 
 
61. (With G. Almkvist) {\it The method of differentiating under the
integral sign}, J. Symbolic Computation {\bf 10}, 571-591 (1990).
 
 
62. {\it The method of creative telescoping}, J. Symbolic Computation
{\bf 11}, 195-204 (1991).
 
 
63. (With D. Foata) {\it Denert's permutation statistic is indeed
Euler-Mahonian}, Studies in Applied Math {\bf 83}, 31-59 (1990).
 
64. (With D. Foata) {\it Multibasic Eulerian polynomials},
Trans. Amer. Math. Soc. {\bf 328}, 843-862 (1991).
 
65. (With R. J. Simpson) {\it Necessary conditions for distinct
covering systems with square-free moduli}, Acta Arithmetica
{\bf 59}, 59-70 (1991).
 
 
66. (With H. S. Wilf) {\it Towards computerized proofs of identities},
Bulletin of the Amer. Math. Soc. {\bf 23}, 77-83 (1990).
 
 
67. {\it Gauss's ${}_2 F_1 (1)$ cannot be generalized to}
${}_2 F_1 (x)$, J. Comp. Appl. Math. {\bf 39},
379-382 (1992).
 
 
68. (With I. Gessel) {\it Random Walk in a Weyl chamber}, Proc.
Amer. Math. Soc. {\bf 115}, 27-31 (1992).
 
 
69. {\it Closed Form (pun intended!)}, 
 in: ``Special volume in memory of Emil Grosswald", M. Knopp
and M. Sheingorn,
eds., Contemporary Mathematics {\bf 143} 579-607, AMS, Providence (1993).
 
 
70. {\it Gert Almkvist's generalization of a mistake of Bourbaki},
 in: ``Special volume in memory of Emil Grosswald", M. Knopp
and M. Sheingorn,
eds., Contemporary Mathematics {\bf 143} 609-612, AMS, Providence (1993).
 
71. {\it Three recitations on Holonomic Systems and 
Hypergeometric Series}, Proceeding of the S\'eminaire
Lotharingien de combinatoire {\bf 24},5-37, IRMA, Strasbourg. (1993)
(To be reprinted in Journal Symbolic Computation.)
 
72. {\it A constant term identity featuring the ubiquitous (and mysterious)
Andrews-Mills-Robbins-Rumsey numbers $\{1,2,7,42,429, ...\}$}, 
J. Combinatorial Theory (ser. A) {\bf 66}, 17-27 (1994).
 
73. {\it A proof of Julian West's conjecture that the number of
2-stack-sortable permutations of length $n$ is}
$2 (3n)! /((2n+1)! (n+1)!)$, Discrete Math. {\bf 102}, 85-93 (1992).
 
74. {\it Identities in search of identity}, J. Theoretical Computer Science
{\bf 117}, 23-38 (1993).
 
75. (With Jane Friedman) A generalization of Odlyzko's conjecture:
the coefficients of 
$(1-q)^{j} /(( 1- q^{2n} ) ... (1- q^{2n+2j} ))$ alternate in
sign,  Proc. Amer. Math. Soc. {\bf 118}, 1013 (1993).
 
76. (With H.S. Wilf) {\it An algorithmic proof theory for hypergeometric
(ordinary and ``q") multisum/integral identities}, Invent. Math. 
{\bf 108}, 575-633 (1992).
 
77. (With S.B. Ekhad) {\it A one-line WZ proof of a formula of Ramanujan
for $\pi$}, in: ``Geometry, Analysis, and Mechanics''
(Volume to honor Archimedes's 2281st birthday), J. M. Rassias, ed.,
107-108. World Scientific, Singapore (1994).
 
78.(with Jane Friedman and Ira Gessel) 
{\it Talmudic lattice path counting}, 
J. Combin. Theory Ser. A {\bf 68}, 215-217 (1994).
 
79. {\it Proof of q-analog of a constant term identity 
conjectured by Forrester}, J. Combinatorial Theory {\bf 66},
311-312 (1994).
 
80. (With H. S. Wilf) {\it Rational function certification of
hypergeometric multi-integral/sum/``q" identities}, 
Bulletin of the Amer. Math. Soc. {\bf 27}, 148-153 (1992).
 
81. (With G.E. Andrews and S.B. Ekhad), {\it A short proof of
Jacobi's formula for the number of representations of an integer
as a sum of four squares}, Amer. Math. Monthly, {\bf 100}, 274-276 (1993).
 
82. {\it  Towards a WZ proof of Mehta's integral}, SIAM J. Math. Anal.
{\bf 25} , 812-814 (1994).
 
83. (With S. B. Ekhad) {\it A  short and elementary,
``formal calculus" proof of the Bieberbach
conjecture (after L. Weinstein)}, Contemporary Math {\bf 178 } 113-115, 
(1995).
 
 
84. (With D. Foata) {\it Combinatorial Proofs of Cappelli's
and Turnbull's Identities from Classical Invariant Theory}, Electronic
J. of Combinatorics

({\tt http://www.combinatorics.org}), {\bf 1}, R1 ( 7 pages) (1994).
 
85. {\it Proof of the alternating sign matrix conjecture}, Elect. J. 
Combinatorics

({\tt http://www.combinatorics.org}), {\bf 3(2)} 
[Foata Festschrift] R13, (50 pages)(1996).
 
86. {\it Theorems for a price: Tomorrow's semi-rigorous mathematical culture},
Notices of the Amer. Math. Soc. {\bf 40 \# 8}, 978-981 (Oct. 1993).
Reprinted: Math. Intell. {\bf 16}, no. 4, 11-14 (Fall 1994).
 
87. {\it Chu's 1303 identity implies Bombieri's 1990 norm-inequality
[Via an identity of Beauzamy and D\'egot]}, Amer. Math. Monthly {\bf 101},
894-895 (1994).
 
88. {\it How Joe Gillis discovered Combinatorial Special Function Theory},
Math. Intell. {\bf 17}, no. 2, 65-66 (Spring 1995). 
 
89. (With L. Ehrenpreis) {\it Two EZ proofs of $\sin^2 z + \cos^2 z =1$},
Amer Math. Monthly {\bf 101}, 691 (1994).
  
90. (With C. Orr), {\it A computer algebra approach to the discrete
Dirichlet problem}, J. Symbolic Comput. {\bf 18}, 87-90 (1994).
 
91. {\it On an identity of Daubechies},
Amer. Math. Monthly {\bf 100}, 487 (1993).
 
92. {\it The J.C.P. Miller Recurrence for Exponentiating a polynomial
and its q-Analog}, J. Difference Eqs. and Appls. {\bf 1}, 57-60 (1995). 
 
93. {\it Proof of the refined alternating sign matrix conjecture},
New York J. of Math. (elec.), 
({\tt http://nyjm.albany.edu/})
{\bf 2}, 59-68 (1996).
 
94. (With D. Foata), {\it The Graphical Major Index}, J. Comp. Appl. Math.,
[specal issue on q-series], 
J. Comput. Applied Math (special issue on q-series)
{\bf 68} 79-101 (1996).
 
95. (With J. Noonan), {\it Counting Permutations with a prescribed
number of ``forbidden" patterns}, Advances in Applied Math. {\bf 17},
381-407 (1996).
 
96. {\it Reverand Charles to the aid of Major Percy and Fields-Medalist
Enrico}, Amer. Math. Monthly {\bf 103}, 501-502 (1996).
 
97. {\it The method of undetermined generalization and specialization
illustrated with Fred Galvin's amazing proof of the Dinitz conjecture},
Amer. Math. Monthly {\bf 103}, 233-240 (1996).
 
98. {\it An explicit formula for the number of solutions of $X^2=0$
in triangular matrices over GF(q)}, 
Elect. J. Comb({\tt http://www.combinatorics.org}). {\bf 3(1)}, R3 
(3 pages)(1996).
 
99. {\it Self-Avoiding Walks, the language of science, and Fibonacci numbers},
J. Stat. Planning and Inference {\bf 54}, 135-138 (1996).
 
100. {\it If $A_n$ has $6n$ dyes in a box, with which he has to fling at
least $n$ sixes, then $A_n$ has an easier task than $A_{n+1}$,
at Eaven Luck}, Amer. Math. Monthly {\bf 103}, 265 (1996).
 
101. (With S. B. Ekhad){\it Curing the Andrews Syndrome},
J. of Difference Equations and Applications {\bf 4}, 299-310 (1997).
 
102. (With T. Amdeberhan)
{\it Hypergeometric Series Acceleration via the WZ method}
Elect. J. of Combinatorics
({\tt http://www.combinatorics.org}), 
{\bf 4(2)} [Wilf Festschrifft volume], R3 (4 pages) (1997).
 
103. (With T. Amdeberhan) {\it q-Apery Irrationality Proofs by q-WZ Pairs}, 
Adv. Appl. Math. {\bf 20}, 275-283, (1998).
 
104. (With D. Foata)
{\it A classic proof of a recurrence for a very classical sequence},
J. Combin. Theory Ser. A {\bf 80}, 380-384 (1997).

105. (With D. Foata)
{\it Combinatorial Proofs of Bass's Evaluations of the Ihara-Selberg 
Zeta function of a Graph}, Trans. Amer. Math. Soc., 
{\bf 351}, 2257--2274 (1999).
 
106. {\it The Abstract Lace Expansion}, Advances in Applied Mathematics,
{\bf 19}, 355-359 (1997).
 
107. (With I. Nemes, M. Petkovsek, and H. S. Wilf)
{\it How to do Monthly Problems on your computer}, Amer. Math. Monthly
{\bf 104}, 505-519 (1997).
 
108. {\it Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and
WOMEN}, Elect. J. of Combinatorics 
({\tt http://www.combinatorics.org})
{\bf 4(2)}, [Wilf Festschrift
volume], R22 (2 pages) (1997).
 
109. {\it A comparison of two methods for random labellings of balls
by vectors of integers},
Advances in Combinatorial Methods and Applications
to Probability and Statistics, N. Balakrishnan, ed., Birkhauser, 1997
(Mohanty Festschrift).
 
110. (With S. B. Ekhad)
{\it Proof of Conway's Lost Cosmological Theorem}
Elect. Res. Announcements of the AMS {\bf 3}, 78-82 (1997).
 
111. {\it 
Math Bite: Proof of an Empirical Observation Made by Amos Oz's character}, 
Math. Magazine {\bf 70 }, 291 (1997).
 
112. {\it How Much Should a Nineteenth-Century French Bastard Inherit},
J. Difference Eq. Appl. {\bf 3}, 385-388 (1998).
 
113. (With C. Krattenthaler)
{\it Proof of a Determinant Evaluation Conjectured by Bombieri, Hunt, and
van der Poorten}, New York J. of Math. (elec.)
({\tt http://nyjm.albany.edu/})
{\bf 3}, 54-102 (1997).

114. {\it Automated Counting of LEGO Towers}, J. Difference Eq. Appl.,
{\bf 5}, 323-333, (1999).
 
115. (With J. Noonan)
{\it The Goulden-Jackson Cluster Method: Extensions, Applications, and
Implementations}, J. Difference Eq. Appl.
{\bf 5}, 355-377, (1999).

116. (With  Scott Ahlgren, Shalosh B. Ekhad, Ken Ono)
{\it A Binomial Coefficient Identity Associated to a Conjecture of
Beukers}, Electronic Journal of Combinatorics

({\tt http://www.combinatorics.org}) {\bf 5}, R10 (1 page) (1998).

117. (With Aaron Robertson)
{\it A 2-Coloring of [1,N] Can Have $(1/22)N^2+O(N)$ Monochromatic
Schur Triples, But Not Less!}, 
Electronic Journal of Combinatorics

({\tt http://www.combinatorics.org}) {\bf 5} R19, (5 pages) (1998).

118. (With Shalosh B. Ekhad)
{\it There Are More Than 2**(n/17) n-Lettered Ternary Square-Free
Words}, J. Integer Sequences (elec.)
({\tt http://www.research.att.com/~njas/jit/}), {\bf 98.1.9} 
(3 pages) (1998).

119. {\it Enumeration Schemes, and More Importantly, 
Their Automatic Generation},
Annals of Combinatorics {\bf 2}, 185-195 (1998).

120. {\it Proof Of A Conjecture Of Chan, Robbins, and Yuen},
ETNA, (Elec. Trans, of Numerical Analysis) (elec.)
({\tt http://etna.mcs.kent.edu/})
{\bf 9}, 147-148, (1999).


121. (With Aaron Robertson and Herb Wilf) 
{\it Patterns and Fractions}, Elec. J. Combinatorics, 
{\bf 6},  ({\tt http://www.combinatorics.org})
R38, (4 pages) (1999).


122. (With S. B. Ekhad)
{\it PLANE GEOMETRY: An Elementary School Textbook (ca. 2050)}, 
Mathematical Intelligencer 
{\bf 21(3)}, 64-70, (1999).

123. {\it Symbol-Crunching with the Transfer-Matrix Method in Order to
 Count Skinny Physical Creatures},
 INTEGERS ({\tt http://www.integers-ejcnt.org}), {\bf 0} A9 (29 pages)
(2000).

124. (With A. Edlin)
{\it The Goulden-Jacskon Cluster Method For Cyclic Words},
Advances in Applied Mathematics  {\bf 25}, 228-232, (2000).

125. {\it The Umbral Transfer-Matrix Method: I. Foundations},
J. Comb. Theory Ser. A
{\bf 91}, 451-463, (Rota memorial issue) (2000).

126. {\it
   How Berger, Felzenbaum, and Fraenkel Revolutionized COVERING
   SYSTEMS The Same Way that George Boole Revolutionized LOGIC},
Elect. J. Combinatorics 8(2) (2001) (special issue in honor of
Aviezri Fraenkel), A1
 ({\tt http://www.combinatorics.org}), (9 pages).

127. (With D. Foata)
{\it Babson-Steingrimsson Statistics Are Indeed Mahonian
(and Sometimes Even Euler-Mahonian)},
 Adv. Appl. Math. {\bf 27} (2001), 390-404

128. {\it Three-Rowed CHOMP}, 
Adv. Appl. Math. {\bf 26} (2001), 168-179.

129. {\it The Umbral Transfer-Matrix Method. III. Counting Animals},
New York J of Mathematics 7(2001), 223-231.

130. (With T. Amdeberhan)
{\it Determinants Through The Looking Glass},
Adv. Appl. Math. {\bf 27} (2001), 225-230

131. {\it The Umbral Transfer-Matrix Method. IV. Counting Self-Avoiding
Polygons and Walks}, Elec. J. Comb. {\bf 8}(1)(2001), (22 pages) R28.

132. {\it The Umbral Transfer-Matrix Method. V. The Goulden-Jackson Cluster
Method for Infinitely Many Mistakes}, INTEGERS, {\bf 2} (2002), 
(10 pages), A5 .

133. (With D. Foata)
{\it The Collector's Brotherhood Problem Using the Newman-Shepp Symbolic
Method}, Algebra Universalis (special Rota memorial issue),
Algebra Universalis (special Rota memorial issue),{\bf 49} (2003), 387-395.

134. {\it ``Real'' Analysis is a Degenerate Case of Discrete Analysis},
Appeared in:
"New Progress in Difference Equations"(Proc. ICDEA 2001), edited by
Bernd Aulbach,
Saber Elaydi, and Gerry Ladas, and publisher by Taylor \& Francis, 
London, 2004. 


135. {\it Computerized Deconstruction}, Adv. Applied Math.
{\bf 30} (2003), 633-654.

136. (With Aaron Robertson, Dan Saracino)
{\it Refined Restricted Permutations}, Annals of Combinatorics.
{\bf 6} (2003), 427-444.

137. {\it Lieber Opa Paul, Ich Bin Auch Ein
Experimental Scientist}, 
Adv. Appl. Math. {\bf 30} (2003), 633-654.

138. {\it Towards a SymbolicComputational Philosophy (and
Methodology!) for Mathematics}, Proc. of the BuchbergerFest,
(Peter Paule, ed.), Springer, to appear.

139. (With Stavros Garoufalidis and Thang TQ Le)
{\it The Quantum MacMahon Master Theorem}, Proc. National Academy of Science, 
{\bf 103} (2006), (no. 38, Sept. 19, 2006), 13928-13931 .

140. {\it Chomp, Recurrences, and Chaos}, 
J. Difference Equations and its Applications
{\bf 8} (2004), 369-378.
[special issue in honor of Saber Elaydi.]

141. (With Xinyu Sun)
On Fraenkel's N-Heap Wythoff Conjecture,
Annals of Combinatorics {\bf 8} (2004). 225-238.

142. (With Mohamud Mohammed) {\it The Markov-WZ Method} 
Elec J. Combinatorics {\bf 11}(2004), R53. (14 pages).

143.{\it Symbolic Moment Calculus I.: Foundations and Permutation
Pattern Statistics}, Annals of Combinatorics {\bf 8} (2004), 369-378.

144. {\it Dave Robbins's Art of Guessing},
Adv. Appl. Math. {\bf 34} (2005), 939-954.

145. (With Mohamud Mohammed) 
{\it Sharp Upper Bounds for the Orders of the Recurrences Outputted by
the Zeilberger and q-Zeilberger Algorithms},
J. Symbolic Computation {\bf 39}  (2005), 201-207.

146. {\it Enumerative and Algebraic Combinatorics},
to appear in: `Princeton Companion of Mathematics',
T.W. Gowers, ed.

147. (With Arthur Benjamin)
Pythagorean Primes and Palindromic Continued Fractions,
INTEGERS {\bf 5(1)} (2005), A30.

148. (With Andrew V. Sills)
{\it Disturbing the Dyson Conjecture (in a GOOD Way)},
J. Experimental Mathematics {\bf 15} (2006), 187-191

149. {\it DECONSTRUCTING the ZEILBERGER algorithm},
J. Difference Equations and its Applications {\bf 11}
(2005), 851-856.

150. (With Moa Apagodu [formerly Mohamud Mohammed])
{\it Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the
Sharpening of Wilf-Zeilberger Theory },
Adv. Appl. Math. {\bf 37} (2006)(Special Regev issue), 139-152

151. {\it Automatc CountTilings}, 
Perosnal Journal of Ekhad and Zeilberger
\hfill\break
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/pj.html}, 2006.

152. {\it The HOLONOMIC ANSATZ I. Foundations and Applications to Lattice
Path Counting}, 
Annals of Combinatorics {\bf 11}(2007), 227-239

153. {\it The HOLONOMIC ANSATZ II.
Automatic DISCOVERY(!) and PROOF(!!) of Holonomic Determinant Evaluations},
Annals of Combinatorics {\bf 11}(2007), 241-247

154. {\it
Symbolic Moment Calculus II.: Why is Ramsey Theory Sooooo Eeeenormoulsy
Hard?}, 
``Combinatorial Number Theory", B. Landman et. al,
editors, in Celebration of the 70th Birthday of Ronald Graham, 
de Gruyter, 2007. (Co-publised in INTEGERS, 7(2)(2007), A34.]


155. (With Shalosh B. Ekhad, Vince Vatter)
{\it A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture},
Perosnal Journal of Ekhad and Zeilberger,
\hfill\break
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/pj.html}, 2006.

156. {\it Symbol Crunching with the Gambler's Ruin Problem}, 
to appear in "Tapas in Experimental Mathematics", Contemporary Mathematics,
a volume edited by Tewodros Amdeberhan and Victor Moll.

157. (With Moa Apagodu)
{\it FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Combinatorics}
"COMPUTER ALGEBRA 2006, Latest Advances in Symbolic Algorithms"
[Abramov Festschrift, dedicated to Sergey Abramov's
60th birthday], edited by Ilias S Kotsireas and Eugene V Zima,
World Scientific, Aug. 2007.

158. (With Arvind Ayyer)
{\it The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points}, 
Electronic J. of Combinatorics {\bf 14(1)} (2007), R19 (8pp).

159. (With Philip Matchett Wood)
{\it A Translation Method for Finding Combinatorial Bijections},
Annals of Combinatorics, to appear.

160. (With Arvind Ayyer)
{\it Two Dimensional Directed Lattice Walks with Boundaries},
to appear in "Tapas in Experimental Mathematics", Contemporary Mathematics,
a volume edited by Tewodros Amdeberhan and Victor Moll.


161. (With  Tewodros Amdeberhan)
{\it 
Trivializing" Generalizations of Some Izergin-Korepin-Type Determinants},
Discrete Mathematics and Theoretical Computer Science {\bf 9} (2007), 203-206.

162. 
{\it An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding},
Appeared in: C.S. Calude ,ed.,
"Randomness \& Complexity, from Leibniz to Chaitin", 
World Scientific, Singapore, Oct. 2007.

163. 
{\it Using  Rota's Umbral Calculus to Enumerate Stanley's P-Partitions},
Adv. Applied Mathematics, to appear.

164. (With Manuel Kauers)
{\it Experiments With a Positivity Preserving Operator},
submitted.

165.
(with Thotsaporn "Aek" Thanatipanonda)
{\it A Symbolic Finite-State Approach For Automated Proving
of Theorems in Combinatorial Game Theory}, submitted.


\bigskip
{\bf BOOKS:}
 
B1. (With M. Petkovsek and H. S. Wilf) {\it A=B}, AK Peters, Wellesley, (1996).

B2. {\it Shalosh B. Ekhad's 2050 Plane Geometry  Text},
(webbook, \hfill\break
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/PG.html})

B3. {\it Shalosh B. Ekhad's Computer-Generated Alphametics},
(webbook, \hfill\break
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/hans/hans.html})

\bigskip
{\bf BOOK REVIEWS:}
 
1. {\it Review of "The Umbral Calculus'' by S.Roman}, Bull. A.M.S., 
{\bf 13}, 73-76(1985).

2. {\it Review of "Proof and Confirmation'' by 
D. Bressoud}, Amer. Math. Monthly, Feb. 2001.

3. {\it Review of "Kepler's Problem'' by G. Szpiro},
Science {\bf 301}, 1086 (Aug. 29, 2003).

4. {\it Review of "Mathematics by Experiments'' by J. Borwein and D. Bailey},
Amer. Sci., March-April 2005, 182-183.
 
\bigskip
{\bf Ph.D. Thesis:}

{\it ``New Approaches and Results in the Theory of Discrete
Analytic Functions''}, Weizmann Institute of Science,
Revovot. Israel, Aug. 1976. Advisor: Harry Dym.
\bigskip
\bigskip
   
\end
 





