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189
Proof of the alternating sign matrix conjecture
, 1995
"... The number of n × n matrices whose entries are either −1, 0, or 1, whose row and column sums are all 1, and such that in every row and every column the nonzero entries alternate in sign, is proved to be [1!4!... (3n −2)!]/[n!(n+1)!... (2n −1)!], as conjectured by Mills, Robbins, and Rumsey. ..."
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Cited by 121 (4 self)
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The number of n × n matrices whose entries are either −1, 0, or 1, whose row and column sums are all 1, and such that in every row and every column the nonzero entries alternate in sign, is proved to be [1!4!... (3n −2)!]/[n!(n+1)!... (2n −1)!], as conjectured by Mills, Robbins, and Rumsey.
A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities
, 1993
"... ..."
Noncommutative Elimination in Ore Algebras Proves Multivariate Identities
 J. SYMBOLIC COMPUT
, 1996
"... ... In this article, we develop a theory of @finite sequences and functions which provides a unified framework to express algorithms proving and discovering multivariate identities. This approach is vindicated by an implementation. ..."
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Cited by 100 (12 self)
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... In this article, we develop a theory of @finite sequences and functions which provides a unified framework to express algorithms proving and discovering multivariate identities. This approach is vindicated by an implementation.
An Extension Of Zeilberger's Fast Algorithm To General Holonomic Functions
 DISCRETE MATH
, 2000
"... We extend Zeilberger's fast algorithm for definite hypergeometric summation to nonhypergeometric holonomic sequences. The algorithm generalizes to differential and qcases as well. Its theoretical justification is based on a description by linear operators and on the theory of holonomy. ..."
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Cited by 90 (5 self)
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We extend Zeilberger's fast algorithm for definite hypergeometric summation to nonhypergeometric holonomic sequences. The algorithm generalizes to differential and qcases as well. Its theoretical justification is based on a description by linear operators and on the theory of holonomy.
Advanced determinant calculus: a complement
 LINEAR ALGEBRA APPL
, 2005
"... This is a complement to my previous article “Advanced Determinant Calculus ” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular probl ..."
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Cited by 89 (8 self)
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This is a complement to my previous article “Advanced Determinant Calculus ” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441– 456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.
Hypergeometric solutions of linear recurrences with polynomial coefficients
 J. Symb. Comput
, 1992
"... We describe algorithm Hyper which can be used to find all hypergeometric solutions of linear recurrences with polynomial coefficients. Let K be a field of characteristic zero. We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms f ..."
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Cited by 79 (10 self)
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We describe algorithm Hyper which can be used to find all hypergeometric solutions of linear recurrences with polynomial coefficients. Let K be a field of characteristic zero. We assume that K is computable, meaning that the elements of K can be finitely represented and that there exist algorithms for carrying out the field operations. Let KN denote the ring of all sequences over K, with addition and multiplication
A Mathematica qAnalogue of Zeilberger's Algorithm for Proving qHypergeometric Identities
, 1995
"... Besides an elementary introduction to qidentities and basic hypergeometric series, a newly developed Mathematica implementation of a qanalogue of Zeilberger's fast algorithm for proving terminating qhypergeometric identities together with its theoretical background is described. To illustr ..."
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Cited by 67 (11 self)
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Besides an elementary introduction to qidentities and basic hypergeometric series, a newly developed Mathematica implementation of a qanalogue of Zeilberger's fast algorithm for proving terminating qhypergeometric identities together with its theoretical background is described. To illustrate the usage of the package and its range of applicability, nontrivial examples are presented as well as additional features like the computation of companion and dual identities.