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… Expand

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.Expand

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… Expand

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… Expand