  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.

Combinatorics