q,t-Catalan numbers and partition numbers

Combinatorics/Partitions Seminar

Meeting Details

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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: 106 McAllister

Date: 10/06/2009

Time: 11:15am - 12:05pm