PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:q,t-Catalan numbers and partition numbers
Seminar:Combinatorics/Partitions Seminar
Speaker:Dr. Kyungyong Lee, Purdue University
Abstract:
The q,t-Catalan numbers naturally occur in the study of Macdonald polynomials, which are an important family of multivariable orthogonal polynomials introduced by Macdonald in 1988 with applications to a wide variety of subjects including Hilbert schemes, harmonic analysis, representation theory, mathematical physics, and algebraic combinatorics. Haiman and Garsia-Haglund proved that they are polynomials of q and t with positive coefficients. Finding coefficients of the n-th q,t-Catalan number is equivalent to counting how many Catalan paths in the n*n square have the same statistics. We give simple upper bounds on coefficients in terms of partition numbers, and describe all coefficients which achieve the upper bounds.

Room Reservation Information

Room Number:MB106
Date:10 / 06 / 2009
Time:11:15am - 12:05pm