Statistics for the (q,t)Catalan NumbersJim HaglundUC San Diego
October 20,

ABSTRACT


In 1994 Garsia and Haiman conjectured that a certain sum of rational functions in two variables q and t (now known as the (q,t)Catalan number) always evaluates to a polynomial with nonnegative coefficients. Based on empirical discoveries, the speaker was led to a stronger form of this conjecture, which involves an explicit expression for the (q,t)Catalan as a sum over Dyck paths. After introducing this conjecture we discuss a proof of it which has recently been found by A. Garsia and the speaker using plethystic identities for Macdonald polynomials. The papers on which this talk is based can be found at http://www.math.ucsd.edu/~jhaglund/ 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

