Constant term identities extending the -Dyson theorem

Authors:
D. M. Bressoud and I. P. Goulden

Journal:
Trans. Amer. Math. Soc. **291** (1985), 203-228

MSC:
Primary 05A30

DOI:
https://doi.org/10.1090/S0002-9947-1985-0797055-8

MathSciNet review:
797055

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Abstract: Andrews [**1**] has conjectured that the constant term in a certain product is equal to a -multinomial coefficient. This conjecture is a -analogue of Dyson's conjecture [**5**], and has been proved, combinatorically, by Zeilberger and Bressoud [**15**]. In this paper we give a combinatorial proof of a master theorem, that the constant term in a similar product, computed over the edges of a nontransitive tournament, is zero. Many constant terms are evaluated as consequences of this master theorem including Andrews' -Dyson theorem in two ways, one of which is a -analogue of Good's [**6**] recursive proof.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0797055-8

Article copyright:
© Copyright 1985
American Mathematical Society