%nsf13d.tex: Project description 
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\def\RightHead{\centerline{NSF Proposal: 
Automated Enumerative Combinatorics
}}
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\centerline{\bf 
Automated Enumerative Combinatorics
}
\bigskip  
\centerline{ \it Doron Zeilberger}
\medskip 
Department of Mathematics, Rutgers University (New Brunswick),
Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway,
NJ 08854-8019.
{\tt zeilberg@math.rutgers.edu} \hfill\break  
{\tt http://www.math.rutgers.edu/\Tilde zeilberg/} .
\bigskip 
{\bf References Cited}

[ABKS] J Ablinger, J Bl\"umlein, S Klein, and C Schneider 
{\it Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams},
Nuclear Physics B - Proceedings Supplements {\bf 205-206} (2010),  110-115. \hfill\break
{\tt http://arxiv.org/pdf/1006.4797} \quad .

[Al] Gert Almkvist, {\it Calabi-Yau differential equations of degree 2 and 3 and Yifan Yang's pullback}, preprint. \hfill\break
{\tt http://arxiv.org/abs/math/0612215} \quad .


[AZ] Moa Apagodu and Doron Zeilberger,
{\it Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the Sharpening of Wilf-Zeilberger Theory},
Adv. Appl. Math. {\bf 37}(2006), (Special issue in honor of Amitai Regev), 139-152. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/multiZ.html}  \quad .


[BZ] Andrew Baxter and Doron Zeilberger,
{\it The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal (Second Edition!)},
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger (refereed by a group of eight world-class experts!), Feb. 4, 2011.
 \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/invmaj.html} \quad .

[BeP] J. B\'etr\'ema and J.-G. Penaud, {\it Mod\`eles avec particules dures, animaux dirig\'e et s\'eries en
variables partiellement commutatives} . \hfill \break
{\tt http://fr.arxiv.org/abs/math/0106210} \quad .

[Bo1] Mikl\'os B\'ona, {\it ``Combinatorics of Permutations''}, Chapman and Hall/CRC, 2004.

[Bo2] Mikl\'os B\'ona, {\it Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps}, 
Journal of Combinatorial Theory, Series A {\bf 80} (1997), 257-272.

[BB] J. Borwein and D. Bailey, {\it Mathematics by Experiment}.
A.K. Peters, Natick, 2004.

[BBCGLM] D. Bailey, J. Borwein, N. Calkin, R. Gingensohn,
D. Luke, and V. Moll, "{\it Experimental Mathematics in Action"},
A.K. Peters, 2007.

[EGZ] Shalosh B. Ekhad, Evangelos Georgiadis and Doron Zeilberger,
{\it How to Gamble If You're In a Hurry},
Journal of Difference Equations and Application, {\bf 19} (2013) , 520-526. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/himurim.html}\quad .

[Gal] J. Gallian, {\it Interview with Doron Zeilberger},
MAA Focus May/June 2007, 14-17. (Available on-line at
{\tt www.maa.org}).

[Gar] Stavros  Garoufalidis, {\it On the characteristic and deformation varieties of a knot},
Geometry and Topology {\bf 7} (2004), 291-309. \hfill\break
{\tt http://arxiv.org/pdf/math.GT/0306230} \quad .

[GL] Stavros  Garoufalidis and T.T.Q. Le, {\it The colored Jones function is q-holonomic},
Geometry and Topology {\bf 9} (2005), 1253-1293. \hfill\break
{\tt http://arxiv.org/pdf/math/0309214} \quad .

[Ge] Ira M. Gessel (1990), {\it Symmetric functions and P-recursiveness},  Journal of Combinatorial Theory, Series A {\bf 53} (1990), 
257-285.  \hfill\break
{\tt http://people.brandeis.edu/\~{}ssel/homepage/papers/dfin.pdf} \quad .

[GZ] Edinah K. Gnang and Doron Zeilberger, {\it Zeroless Arithmetic: Representing Integers ONLY using},
to appear in J. Difference Equations and Applications. \hfill\break
{\tt http://math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/arif.html} \quad .

[Gu] Jes\'us Guillera, { \it A new Ramanujan-like series for $1/\pi^2$},  Ramanujan J.  {\bf 26}(2011), 369 - 374. \hfill\break
{\tt http://arxiv.org/abs/1003.1915} \quad .

[GR] Jes\'us Guillera and Mat Rogers, {\it Mahler measure and the WZ-algorithm},
Proc. of the Amer. Math. Soc., to appear. \hfill\break
{\tt http://arxiv.org/abs/1006.1654} \quad .

[HNTT] Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
{\it Holonomic gradient method for the distribution function of the largest root of a Wishart matrix},
Journal of Multivariate Analysis {\bf 117}(2013), 296-312. \hfill\break  
{\tt http://arxiv.org/abs/1201.0472} \quad .

[HZ] Emilie Hogan and Doron Zeilberger,
{\it A New Algorithm for Proving Global Asymptotic Stability of Rational Difference Equations},
Journal of Difference Equations and Applications {\bf 18}(2012), 1853-1873. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/gas.html} \quad .

[KKZ]  Christoph Koutschan, Manuel Kauers, and Doron Zeilberger,
{\it A Proof Of George Andrews' and David Robbins' q-TSPP Conjecture},
Proceedings of the National Academy of Science, {\bf 108 \#6} (Feb. 8, 2011), 2196-2199. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/qtsppRig.html} \quad .

[KT] Christoph Koutschan and Thotsaporn Thanatipanonda, {\it  Advanced Computer Algebra for Determinants},
Annals of Combinatorics, to appear.  \hfill\break
{\tt http://arxiv.org/abs/1112.0647} \quad .
     
[K1] C. Krattenthaler, {\it Advanced Determinant Calculus},
S\'em. Lothar. Comb. {\bf 42} (1999), B42q.
(``The Andrews Festschrift'', D. Foata and G.-N. Han(eds.)). \hfill\break
{\tt http://arxiv.org/abs/math/9902004}

[K2] C. Krattenthaler, {\it Advanced Determinant Calculus:
A Complement}, Linear Algebra Appl. {\bf 411}(2005), 68-166. \hfill\break
{\tt http://arXiv.org/abs/math.Co/0503507} \quad .

[NZ] Brian Nakamura and Doron Zeilberger,
{\it Using Noonan-Zeilberger Functional Equations to Enumerate (in Polynomial Time!) Generalized Wilf Classes},
Advances in Applied Mathematics {\bf 50} (2013), 356-366.  \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/Gwilf.html} \quad .

[O] Soichi Okada, {\it On the generating functions for certain
classes of plane partitions}, J. Comb. Theory Ser. A {\bf 53}(1989), 1-23.
 
[PWZ] Marko Petkovsek, Herbert Wilf, and Doron Zeilberger,
{\it ``A=B''}, AK Peters, Wellesley, (1996).
{\tt Web Page: http://central.cis.upenn.edu/\Tilde wilf/AeqB.html}\quad .

[R] John Riordan, ``{\it Introduction to Combinatorial Analysis}'', John Wiley, 1958. Reprinted by Dover, 2002.

[SZ] Andrew V. Sills and Doron Zeilberger,
{\it Rademacher's Infinite Partial Fraction Conjecture is (almost certainly) False},
Journal of Difference Equations and Applications {\bf 19} (2013), 680-689. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/hans.html} \quad .

[St] Richard Stanley, {\it A baker's dozen of conjectures concerning
plane partitions}. In {\it ``Combinatoire \'enum\'erative''}, ed.
G. Labelle and P. Leroux. Lecture Notes in Mathematics {\bf 1234} (1986), 285-293. Springer Verlag, New York. \hfill\break
{\tt http://www-math.mit.edu/\~{}rstan/pubs/pubfiles/67.pdf} \quad .

[Su] Zhi-Wei Sun, {\it Super congruences and Euler numbers},
China Mathematics {\bf 54} (2011), 2509-2535. \hfill\break
{\tt http://arxiv.org/abs/1001.4453} \quad .

[T] Marko Thiel,
{\it The inversion number and the major index are asymptotically jointly normally distributed on words},
preprint. \hfill\break
{\tt http://arxiv.org/abs/1302.6708} \quad .

[WZ] Herbert S. Wilf and Doron Zeilberger, {\it An algorithmic proof theory for hypergeometric (ordinary and ``q'') multisum/integral identities},
Invent. Math. {\bf 108}(1992), 575-633. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/multiwz.html} \quad .

[V] Vince Vatter,  {\it Enumeration schemes for restricted permutations},
Combinatorics, Probability and Computing {\bf 17}(2008), 137-159. \hfill\break
{\tt http://www-groups.mcs.st-andrews.ac.uk/\~{}vince/publications/wilfplus/} \quad .

[Z1] Doron Zeilberger,
{\it The HOLONOMIC ANSATZ I. Foundations and Applications to Lattice
Path Counting}, 
Annals of Combinatorics {\bf 11}(2007), 227-239 . \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/ansatzI.html} \quad .

[Z2] Doron Zeilberger,
{\it The HOLONOMIC ANSATZ II.
Automatic DISCOVERY(!) and PROOF(!!) of Holonomic Determinant Evaluations},
Annals of Combinatorics {\bf 11}(2007), 241-247 . \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/ansatzII.html} \quad .

[Z3] Doron Zeilberger,
{\it An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding},
in: C.S. Calude, ed.,
``Randomness \& Complexity, from Leibniz to Chaitin", 
World Scientific, Singapore, Oct. 2007.  \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/enquiry.html} \quad .

[Z4] Doron Zeilberger,
{\it Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture},
J. of Difference Equations and Applications {\bf 17}(2011), 375-386. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/collatz.html} \quad .

[Z5] Doron Zeilberger,
{\it The Amazing $3^n$ Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his \'Ecole Bordelaise gang]},
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Aug 10, 2012. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/bordelaise.html} \quad .

[Z6] Doron Zeilberger, {\it Enumeration Schemes, and More Importantly, Their Automatic Generation},
Annals of Combinatorics {\bf 2}(1998), 185-195 . \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/wilf.html}  \quad .

[Z7] Doron Zeilberger,
{\it On Vince Vatter's Brilliant Extension of Doron Zeilberger's Enumeration Schemes for Counting Herb Wilf's Classes},
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, Dec. 29, 2006. \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/vatter.html} \quad .

[Z8] Doron Zeilberger,
{\it Automated Counting of Towers \'A La Bordelaise [Or: Footnote to p. 81 of the Flajolet-Sedgewick Chef-d'oeuvre]},
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger,  Dec. 17, 2012  . \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/migdal.html} \quad .

[Z9] Doron Zeilberger, {\it The Automatic Central Limit Theorems Generator (and Much More!)},
Advances in Combinatorial Mathematics: Proceedings of the Waterloo Workshop in Computer Algebra 2008 in honor of Georgy P. Egorychev'', 
chapter 8, pp. 165-174, (I.Kotsireas, E.Zima, eds. Springer Verlag, 2009) . \hfill\break
{\tt http://www.math.rutgers.edu/\~{}zeilberg/mamarim/mamarimhtml/georgy.html} \quad .

[Zu] Wadim Zudilin, {\it Ramanujan-type supercongruences},
Journal of Number Theory {\bf 129}(2009), 1848–1857. \hfill\break
{\tt http://arxiv.org/pdf/0805.2788} \quad .

\end
