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Probability and Combinatorics

Tuesday, September 24, 2002 - 4:30pm

Jim Haglund

Penn

Location

University of Pennsylvania

DRL 4N30

We show how statistics on Dyck paths for the q,t-Catalan polynomial have a natural extension to Motzkin paths (which are Dyck paths with diagonal steps in addition to N and E steps). The result is a polynomial in q,t which when t=1 and t=1/q give the two q-analogs of the Schroder polynomial introduced by Bonin, Shapiro and Simion. A recurrence and explicit formula are derived by a combinatorial argument. We conjecture our polynomials are symmetric in q and t and discuss a possible interpretation in terms of representation theory. This is joint work with Eric Egge, Darla Kremer and Kendra Killpatrick.