D. Zeilberger

Publications374
h-index38
Citations6,740
Highly Influential Citations598
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An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities
SummaryIt is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible…
A holonomic systems approach to special functions identities
The Method of Creative Telescoping
A fast algorithm for proving terminating hypergeometric identities
The Method of Differentiating under the Integral Sign
Proof of the alternating sign matrix conjecture
TLDR
The number of matrices whose entries are either $-1, $0, or $1$, and such that in every row and every column the non-zero entries alternate in sign, is proved to be 1-4-2-3-2, as conjectured by Mills, Robbins, and Rumsey.
Denert's permutation statistic is indeed Euler-Mahonian
Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
Random walk in a Weyl chamber
The classical Ballot problem that counts the number of ways of walking from the origin and staying within the wedge x 1 ≥x 2 ≥...≥x n (which is a Weyl chamber for the symmetric group), using positive…
The Goulden—Jackson cluster method: extensions, applications and implementations
Th powerful (and so far under-utilized) Goulden—Jackson Cluster method for finding the generating function for the number of words avoiding, as factors, the members of a prescribed set of ‘dirty…
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