Some asymptotic results on q-binomial coefficients

Abstract

We look at the asymptotic behavior of the coefficients of the $q$-binomial coefficients (or Gaussian polynomials) ${\left(\genfrac{}{}{0ex}{}{a+k}{k}\right)}_q$, when $k$ is fixed. We give a number of results in this direction, some of which involve Eulerian polynomials and their generalizations.

A few revisions in response to the referee's comments. 12 pages. To appear in the Annals of Combinatorics