q-Catalan numbers and the Shapiro-Catalan convolution

Combinatorics/Partitions Seminar

Meeting Details

For more information about this meeting, contact Barbara Baum.

Speaker: Dr. George Andrews, Department of Mathematics, The Pennsylvania State University

Abstract: Recently, T. Koshy published a book entitled "Catalan Numbers". On page 123, he provides a little known identity of Catalan numbers that was found by L. Shapiro in 2002. R. Stanley has asked for a combinatorial proof of Shapiro's identity. In this talk, we discuss a q-analog of Catalan numbers from J. Comb. Th. (A), 44(1987), 267-273. We shall present the motivation and background of these q-Catalan numbers, and, if time allows, we shall allude to how these allow a combinatorial proof of the q-analog of the Shapiro identity (and thus of Shapiro's identity itself).

Room Reservation Information

Room Number: 106 McAllister

Date: 01/13/2009

Time: 11:15am - 12:05pm