2007/01/02 by L. M. Butler, Lynne M. Butler, Butler, L. M. +3
Mathematics · #05A05 #05A10 #05A20 #11B65 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A10 #msc:05A20 #msc:11B65
paper · pdf · doi:10.48550/arxiv.math/0701065
arxiv created 2007/01/02 · openalex publication_date 2007/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.