In 1988, Macdonald introduced a family of symmetric functions with two variables that are known as the Macdonald polynomials which becomes a basis for the space of symmetric functions. Also, he defined the integral form Macdonald polynomials by multiplying certain polynomials to the Macdonald polynomials and he conjectured that the coefficients of the integral form Macdonald polynomials in modified Schur expansion are polynomials in q and t with nonnegative coefficients. In this talk, we consider the pure Schur expansion of integral form Macdonald polynomials and construct a combinatorial formula for the Schur coefficients in the hook case.
Graduate Student Combinatorics Seminar
Wednesday, April 8, 2009 - 12:30pm
Meesue Yoo
University of Pennsylvania