Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
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
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.