A simple proof of the Zeilberger–Bressoud 𝑞-Dyson theorem

Abstract

As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-analogue of Dyson’s conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.