We observe that many special functions are solutions of so-called holonomic systems. Bernsteinâ€™s deep theory of holonomic systems is then invoked to show that any identity involving sums andâ€¦ (More)

The result was that, when guys at MIT or Princeton had trouble doing a certain integral, it was because they couldnâ€™t do it with the standard methods they had learned in school. If it was contourâ€¦ (More)

The classical Ballot problem that counts the number of ways of walking from the origin and staying within the wedge xx > X2 > â– â– â– > xâ€ž (which is a Weyl chamber for the symmetric group), usingâ€¦ (More)

In Zeilberger (preprint) it was shown that Joseph N. Bernstein's theory of holonomic systems (Bernstein, 1971; Bjork, 1979) forms a natural framework for proving a very large class of specialâ€¦ (More)

Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order n equals A(n) := 1!4!7! Â· Â· Â· (3n âˆ’ 2)! n!(n + 1)! Â· Â· Â· (2n âˆ’ 1)! . Mills,â€¦ (More)

Superficially, this article, dedicated with friendship and admiration to Amitai Regev, has nothing to do with either Polynomial Identity Rings, Representation Theory, or Young tableaux, to all ofâ€¦ (More)

Once on the forefront of mathematical research in America, the asymptotics of the solutions of linear recurrence equations is now almost forgotten, especially by the people who need it most, namelyâ€¦ (More)

The 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 'dirtyâ€¦ (More)