Further results on the divisibility of q-trinomial coefficients

2022/07/13 by Ji-Cai Liu, Weiwei Qi, Liu, Ji-Cai +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2207.06054

Abstract

We study divisibility for the q-trinomial coefficients τ₀(n,m,q), T₀(n,m,q) and T₁(n,m,q), which were first introduced by Andrews and Baxter. In particular, we completely determine τ₀(an,bn,q), T₀(an,bn,q) and T₁(an,bn,q) modulo the square of the cyclotomic polynomial Φ_n(q) for (a,b)=(m,m-1).

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