Constant term identities extending the 𝑞-Dyson theorem

Bressoud, D. M.; Goulden, I. P.

doi:10.1090/S0002-9947-1985-0797055-8

Constant term identities extending the $q$-Dyson theorem
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by D. M. Bressoud and I. P. Goulden PDF

Trans. Amer. Math. Soc. 291 (1985), 203-228 Request permission

Abstract:

Andrews [1] has conjectured that the constant term in a certain product is equal to a $q$-multinomial coefficient. This conjecture is a $q$-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’ $q$-Dyson theorem in two ways, one of which is a $q$-analogue of Good’s [6] recursive proof.

References

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Andrews’

Dyson conjecture

Andrews’

Dyson conjecture

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