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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Constant term identities extending the $ q$-Dyson theorem


Authors: D. M. Bressoud and I. P. Goulden
Journal: Trans. Amer. Math. Soc. 291 (1985), 203-228
MSC: Primary 05A30
MathSciNet review: 797055
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0797055-8
Article copyright: © Copyright 1985 American Mathematical Society