Some q-Supercongruences for the truncated q-trinomial coefficients

TL;DR

This paper establishes new q-supercongruences for truncated q-trinomial coefficients, extending the understanding of their properties and potential applications in combinatorics and mathematical physics.

Contribution

It introduces novel q-supercongruences for truncated q-trinomial coefficients, a topic not previously explored in this context.

Findings

Derived new q-supercongruences for truncated q-trinomial coefficients

Extended the theoretical framework of q-series and supercongruences

Potential implications for combinatorics and statistical mechanics

Abstract

In 1987, Andrews and Baxter introduced six kinds of $q$-trinomial coefficients in exploring the solution of a model in statistical mechanics. In this paper, we give some $q$-supercongruences for the truncated forms of these polynomials.