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Probability and Combinatorics

Tuesday, April 15, 2003 - 4:30pm

Jim Haglund

Penn

Location

University of Pennsylvania

DRL 4N30

Recently the speaker, E. Egge, K. Killpatrick and D. Kremer introduced a two-parameter polynomial S_{n,d}(q,t), which is defined as a sum of statistics over lattice paths with d diagonal steps and n-d North and East steps. For d=0 it reduces to the (q,t)-Catalan polynomial. They conjectured that it has an interpretation in terms of hook shapes and the representation theory of the space of Diagonal Harmonics. In this talk we describe a proof of this conjecture, which uses plethystic symmetric function identities.