Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: A Combinatorial Model for the Macdonald Polynomials

Speaker: **Jim Haglund**, University of Pennsylvania

Date: December 9, 2004 4:30-5:30pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We discuss a recent result of M. Haiman, N. Loehr, and the speaker, which gives a combinatorial formula, involving generalizations of the permutation statistics maj and inv, for the coefficient of a monomial in the modified Macdonald polynomial. Consequences of the formula include a new, short proof of Lascoux and Schtzenberger's cocharge description for Hall-Littlewood polynomials. The formula was first discovered by the speaker using experimental methods, and we describe the sequence of steps which led to the statistics.