A note on log-convexity of q-Catalan numbers

被引：14

作者：

Butler, Lynne M. ^{[1
]}

Flanigan, W. Patrick ^{[2
]}

机构：

[1] Haverford Coll, Dept Math, Haverford, PA 19041 USA

[2] Blazek & Gebhardt Retirement Serv Inc, Lutherville Timonium, MD 21093 USA

来源：

ANNALS OF COMBINATORICS | 2007年 / 11卷 / 3-4期

关键词：

Catalan; log-convex; Gaussian; log-concave; q-log-convex; q-log-concave;

D O I：

10.1007/s00026-007-0324-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：369 / 373

页数：5