%0 Journal Article
%T A q-rious positivity
%A S. Ole Warnaar
%A Wadim Zudilin
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00010-010-0055-9
%X 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.
%U http://arxiv.org/abs/1003.1999v1