## 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 Dysonâ€™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 Andrewsâ€™ $q$-Dyson theorem in two ways, one of which is a $q$-analogue of Goodâ€™s [

**6**] recursive proof.

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## Additional Information

- © Copyright 1985 American Mathematical Society
- 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