Standard fillings to parking functions

Abstract

The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating function of parking functions. In this paper we present a weight-preserving injection from standard fillings to parking functions for certain cases.

Keywords

• diagonal harmonics
• macdonald polynomials
• parking functions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]