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RIGOROUS EXPERIMENTAL COMBINATORICS
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\centerline{\bf 
RIGOROUS EXPERIMENTAL COMBINATORICS: References Cited
}



[Aom] K. Aomoto, {\it Jacobi polynomials associated with Selberg
integrals}, SIAM J. Math. Anal. {\bf 18}(1987), 545-549

[AZ] A. Ayyer and D. Zeilberger, 
{\it A bijectionist approach to the the Razumov-Stroganov
conjecture}, in preparation. (To be posted in {\tt arxiv.org}
and Zeilberger's website)

[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.

[BCG] E. Berlekamp, J. Conway, and R. Guy, 
``{\it Winning Ways for your Mathematical Plays}'', Academic 
Press, New York, 1982. 

[Bour1] J. Bourgain, {\it On triples in arithmetical
progression}, Geom. Funct. Anal. {\bf 9} (1999), 968-084.

[Bour2] J. Bourgain, {\it Roth's theorem on progression revisited}
J. Math. Anal. {\bf 104} (2008), 155-192.

[Bous] M. Bousquet-M\'elou, ``{\it Rapport Scientifique
pour obtenir l'Habilation \`a diriger des Recherches}'',
avalable from
{\eighttt http://dept-info.labri.u-bordeaux.fr/\Tilde bousquet/}.

[Bre] D. M. Bressoud, {\it ``Proofs and Confirmations''},
Math. Assoc. America and Cambridge University Press (1999).

[BS] E. Babson and E. Steingr\'\i msson,
{\it Generalized permutation patterns and a classification
of the Mahonian statistics}, {\sl S\'em. Loth. Comb. }
[{\tt http://mat.univie.ac.at/$\sim$slc/}]
{\bf 44 }, 2000, B44b, 18~pp.

[CS] Fr\'ed\'eric Chyzak and Bruno Salvy,
{\it Non-commutative elimination in Ore algebras proves
multivariate identities}, J. of Symbolic Computation
{\bf 26} (1998), 187-227.

[DW] J. D\'esarm\'enien and M. Wachs, {\it Descent
classes of permutations with a given number of fixed points},
J. Comb. Ser. A {\bf 64} (1993), 311-328.

[Eri] J. Erickson, {\it New Toads and Frogs 
Results}, in: ``Games of No Chance'', R. Nowakowski, ed., 
(Proc.  of ``Combinatorial Games at MRSRI, 1994''), 299-310,
Cambridge University Press, 1996.

[Fis] I. Fischer, {\it A new proof of the refined
alternating sign matrix theorem}, J. Combin. Theory
Ser. A {\bf 114} (2007), 253-264.

[Foa1] D. Foata, {\it On the Netto inversion 
number of a sequence}, Proc. Amer. Math. Soc. {\bf 19} (1968),
236-240.

[Foa2] D. Foata, {\it Distributions eul\'eriennes
et mahonniennes sur le
groupe des permutations}, in : ``{\sl Higher Combinatorics}'',
M. Aigner, ed.,Berlin, 1976, 27-49.

[FT] M. Fisher and H. Temperley, {\it Dimer Problems in Statistical
Mechanics-an exact result}, Philos. Mag. {\bf 6} (1961), 1061-1063.

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

[GG] A. Garsia and I. Gessel,
{\it Permutations Statistics and
Partitions}, Adv. in Math. {\bf 31} (1979), 288--305.
 
[GJ] I. Goulden  and D.M. Jackson,
{\it An inversion theorem for cluster decompositions of
sequences with distinguished subsequences},
J. London Math. Soc.(2){\bf 20} (1979), 567-576.

[Gow] W.T. Gowers, {\it A new proof of Szemer\'edi's theorem},
Geom. Funct. Anal. {\bf 11} (2001), 465-588.

[Kas] 
P. W. Kasteleyn, {\it The statistics of dimers on a lattice: I. The number of
dimer arrangements in a quadratic lattice}, Physica {\bf 27} (1961), 1209-1225.

[KBI] V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, 
{\it ``Quantum Inverse Scattering and Correlation Function''},
Cambridge University Press, Cambridge, England, 1993.

[Ku1] G. Kuperberg, {\it Another proof of the alternating sign matrix
conjecture}, Inter. Math. Res. Notes {\bf 1996}, no. 3, 139-150.

[Ku2] G. Kuperberg, {\it Symmetry classes of alternating sign matrices
under one roof}, Ann. of Math. (2) {\bf 156} (2002), 835-866.


[Mac] P. A. MacMahon, {\sl Combinatory
Analysis,} {\rm vol.~1 and~2}. Cambridge, Cambridge Univ. Press,
1915 (Reprinted by Chelsea, New York,
1955).

[NZ] J. Noonan and D. Zeilberger,
{\it The Goulden-Jackson Cluster Method: Extensions, Applications, and
Implementations}, J. Difference Eq. Appl. {\bf 5}, 355-377, (1999).

[Oka] S. Okada, {\it On the generating functions for certain
classes of plane partitions}, J. Comb. Theory, Series A
{\bf 53} (1989), 1-23.

[Po1] G. Polya, ``{\it How to Solve it}", Doubleday, 1957.

[Po2] G. Polya, ``{\it Mathematics and plausible reasoning}", two volumes,
Princeton Univ. Press, 1968.

[PWZ] M. Petkovsek, H. S. Wilf, and D. Zeilberger,
``{\it A=B}", AK Peters, Wellesley, (1996).


[RS] A.V. Razumov and Yu.G. Stroganov, {\it Combinatorial nature of ground state vector
$O(1)$ loop model}, Theor. Math. Physics {\bf 138} (2004), 395-400. {\tt math.CO/0104216}.


[Sta1] R. Stanley {\it Differentiably finite power series},
European J. Combin. {\bf 1} (1980), 175-188.

[Sta2] R. Stanley, {\it A baker's dozen of conjectures concerning
plane partitions}. in: {\it Combinatoire \'enum\'erative}, 
G. Labelle and P. Leroux., eds.,  Lecture Notes in Mathematics
{\bf 1234}, 285-293. Springer Verlag, New York.

[Sta3] R. Stanley, {\it Symmetries 
of plane partitions}, J. Comb. Theory, Series A
{\bf 43} (1986), 103-113.

[Ste] J. Stembridge, {\it The enumeration of totally
symmetric plane partitions}, Advances in Mathematics {\bf 111},
227-243 (1995).

[SW] J. Sareshian and M. Wachs, {\it $q$-Eulerian
polynomials: excedance number and major index},
Elec. Res. Announc. Amer. Math. Soc. {\bf 13} (2007), 33-45.

[SZ] B.Salvy and P. Zimmermann 
{\it Gfun: a Maple package for the manipulation of generating and holonomic 
functions in one variable}, ACM Trans. Math. Soft. {\bf 20}(1994).

[Sze] E. Szemer\'edi, {\it On sets of integers containing no
$k$ elements in arithmetic progressions}, Acta Arith. {\bf 27}
(1975), 299-345.

[Wei]
E. W. Weisstein et al.,  ``Ansatz.'' From MathWorld--A Wolfram Web Resource. \hfill\break
{\tt http://mathworld.wolfram.com/Ansatz.html} 

[Wil] H. Wilf, {\it Mathematics: An Experimental Science},
in: ``Princeton Companion of Mathematics'', T. Gowers, ed.,
991-999, Princeton University Press, 2008. 

[WZ] H. Wilf and D. Zeilberger,
 {\it An algorithmic proof theory for hypergeometric
(ordinary and ``q") multisum/integral identities}, Invent. Math. 
{\bf 108}, 575-633 (1992).

[Z1] D. Zeilberger, 
{\it The Joy of Brute Force:
The covariance of the number of inversions and the major Index},
Personal Journal of Ekhad and and Zeilbeger, \hfill\break
{\eighttt http://www.math.rutgers.edu/\Tilde zeilberg/pj.html \quad .}

[Z2] D. Zeilberger, 
{\it A Holonomic systems approach to special functions
identities}, J. of Computational and Applied Math. {\bf 32},
321-368 (1990).

[Z3] D. Zeilberger,
{\it Proof of the alternating sign matrix conjecture}, Elect. J. 
Combinatorics \hfill\break
({\tt http://www.combinatorics.org}) 
{\bf 3(2)} [Foata Festschrift] R13, (50 pages)
(1996).
  
[Z4]  D. Zeilberger,
{\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).





 



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