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It is shown that every 'proper-hypergeometric ' multisum/integral identity, or q-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof.â€¦ (More)

- Doron Zeilberger
- Discrete Mathematics
- 1990

An algorithm for proving terminating hypergeometric identities, and thus binomial coefficients identities, is presented. It is based upon Gosper's algorithm for indefinite hypergeometric summation. Aâ€¦ (More)

- Gert Almkvist, Doron Zeilberger
- J. Symb. Comput.
- 1990

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)

- Doron Zeilberger
- Electr. J. Comb.
- 1996

Gert Almkvist, Noga Alon, George Andrews, Anonymous, Dror Bar-Natan, Francois Bergeron, Nantel Bergeron, Gaurav Bhatnagar, Anders BjÃ¶rner, Jonathan Borwein, Mireille Bousquest-MÃ©lou, Francescoâ€¦ (More)

- Doron Zeilberger
- J. Symb. Comput.
- 1991

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)

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)

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)

- Moa APAGODU, Doron Zeilberger
- 1940

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)

- Doron Zeilberger
- 1996

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· (3nâˆ’ 2)! n!(n+ 1)! Â· Â· Â· (2nâˆ’ 1)! . Mills, Robbins,â€¦ (More)

- Dominique Foata, Doron Zeilberger
- J. Comb. Theory, Ser. A
- 1997

and stated that ``no direct combinatorial proof of this formula seems to be known.'' The purpose of this note is to fill this gap. The present proof reflects the ideas of our great master, M.-P. Schuâ€¦ (More)