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Probability and Combinatorics

Tuesday, November 1, 2005 - 4:00pm

Mahir Bilen Can

University of Pennsylvania

Location

University of Pennsylvania

DRL 4N30

The q,t-Catalan series have been extensively studied by many authors including Haglund, Haiman, Garsia, Loehr and others. Tracing their origin back we see that they have arisen in many different contexts including symmetric functions, algebraic geometry, and representation theory. Combinatorially they are defined as the weighted sums of Dyck Paths with respect to suitable statistics called area and bounce or equivalently area and dinv. Recently, Nick Loehr and Greg Warrington have extended these statistics to square lattice paths and conjectured an interpretation in terms of the nabla operator in symmetric function theory. In this talk we are going to prove their connjecture.