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

Ji-Cai Liu; Wei-Wei Qi

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

Number Theory 2022-07-14 v1 Combinatorics

Authors: Ji-Cai Liu , Wei-Wei Qi

Abstract

We study divisibility for the $q$ -trinomial coefficients $\tau_0(n,m,q)$ , $T_0(n,m,q)$ and $T_1(n,m,q)$ , which were first introduced by Andrews and Baxter. In particular, we completely determine $\tau_0(an,bn,q)$ , $T_0(an,bn,q)$ and $T_1(an,bn,q)$ modulo the square of the cyclotomic polynomial $\Phi_n(q)$ for $(a,b)=(m,m-1)$ .

Keywords

q-trinomial coefficients divisibility cyclotomic polynomial andrews-baxter coefficients modular arithmetic

Cite

@article{arxiv.2207.06054,
  title  = {Further results on the divisibility of $q$-trinomial coefficients},
  author = {Ji-Cai Liu and Wei-Wei Qi},
  journal= {arXiv preprint arXiv:2207.06054},
  year   = {2022}
}

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11 pages

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

Abstract

Keywords

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