Larry X. W. Wang

Recurrence Relations for Strongly q-Log-Convex Polynomials

We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly q-log-convex. We also prove that the Bessel transformation preserves log-convexity. Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, P. R. China e-mail: chen@nankai.edu.cn wxw@cfc.nankai.edu.cn yang@nankai.edu.cn Received by the editors June 27, 2008. Published electronically February 10, 2011. This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education and the National Science Foundation of China. AMS subject classification: 05A20, 05E99.

Families of Sets with Intersecting Clusters

A family of

The limiting distribution of the coefficients of the

k

q

-subsets

-Catalan numbers

A_1,A_2,\ldots,A_d

Finite differences of the logarithm of the partition function

on

Higher order log-concavity in Euler's difference table

[n]=\{1,2,\ldots,n\}

The Corners of Core Partitions

is called a

Moments about the mean of the size of a self-conjugate (s,t)-core partition

(d,c)

Interlacing log-concavity of the derangement polynomials and the Eulerian polynomials

-cluster if the union