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

TL;DR

This paper provides a concise polynomial proof of the Zeilberger-Bressoud q-Dyson theorem using the Combinatorial Nullstellensatz, simplifying the understanding of this important combinatorial identity.

Contribution

It introduces a new, simplified proof method for the q-Dyson theorem based on polynomial techniques, offering an alternative to previous complex proofs.

Findings

Proof confirms the q-Dyson conjecture using polynomial methods

Simplifies the understanding of the q-Dyson theorem

Demonstrates the power of the Combinatorial Nullstellensatz in combinatorics

Abstract

As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the q-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.