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An Injection From Standard Fillings To Parking Functions, Elizabeth Niese
An Injection From Standard Fillings To Parking Functions, Elizabeth Niese
Elizabeth Niese
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.