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arXiv · 2207.06054

Further results on the divisibility of $q$-trinomial coefficients

Ji-Cai Liu·Wei-Wei Qi
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Abstract

We study divisibility for the $q$-trinomial coefficients $τ_0(n,m,q)$, $T_0(n,m,q)$ and $T_1(n,m,q)$, which were first introduced by Andrews and Baxter. In particular, we completely determine $τ_0(an,bn,q)$, $T_0(an,bn,q)$ and $T_1(an,bn,q)$ modulo the square of the cyclotomic polynomial $Φ_n(q)$ for $(a,b)=(m,m-1)$.

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Ji-Cai Liu, Wei-Wei Qi. 2022-07-13. Further results on the divisibility of $q$-trinomial coefficients. https://arxiv.org/abs/2207.06054

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