一种积极的态度
A q-rious positivity
摘要：
对于整数$0\le m\le n$，已知$q$ -二项式系数$\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$是具有非负整数系数的多项式.这很容易从$q$ -二项式定理，或$\qbinom{n}{m}$的许多组合解释。在本文中，我们猜想一个算术动机的推广的非负性质的产品的比率$q$ -因子，碰巧是多项式。
英文摘要：
The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients. This readily follows from the $q$-binomial theorem, or the many combinatorial interpretations of $\qbinom{n}{m}$. In this note we conjecture an arithmetically motivated generalisation of the non-negativity property for products of ratios of $q$-factorials that happen to be polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
