For more information about this meeting, contact Mary Anne Raymond.
| Title: | q,t-Catalan numbers and partition numbers |
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| Seminar: | Combinatorics/Partitions Seminar |
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| Speaker: | Dr. Kyungyong Lee, Purdue University |
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| Abstract: |
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| 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 |
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| Date: | 10 / 06 / 2009 |
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| Time: | 11:15am - 12:05pm |
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