Constant term identities extending the 𝑞-Dyson theorem

Abstract

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