For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov . In two special cases, we show that the coefficients of this function when expanded in the complete homogeneous basis are given in terms of the (reduced) type of k-divisible noncrossing partitions. Our work extends Haiman's notion of a parking function symmetric function [5, 10].
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics