A note on log-convexity of q-Catalan numbers
Combinatorics
2007-05-23 v1
Abstract
The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted.
Cite
@article{arxiv.math/0701065,
title = {A note on log-convexity of q-Catalan numbers},
author = {L. M. Butler and W. P. Flanigan},
journal= {arXiv preprint arXiv:math/0701065},
year = {2007}
}