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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
The Method of Creative Telescoping
Proof of the alternating sign matrix conjecture
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.
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