A new recursion for three-column combinatorial Macdonald polynomials

Authors

Elizabeth Niese, Marshall UniversityFollow

Document Type

Article

Publication Date

1-2013

Abstract

The Hilbert series of the Garsia–Haiman module M_μ can be described combinatorially as the generating function of certain fillings of the Ferrers diagram of μ where μ is an integer partition of n . Since there are n ! fillings that generate , it is desirable to find recursions to reduce the number of fillings that need to be considered when computing combinatorially. In this paper, we present a combinatorial recursion for the case where μ is an n by 3 rectangle. This allows us to reduce the number of fillings under consideration from (3n)! to (3n)!/(3!ⁿn!).

Comments

This is the author’s submitted manuscript.

The published version of record is available at http://dx.doi.org/10.1016/j.jcta.2012.07.008.

© 2012 Elsevier Inc. All rights reserved

Recommended Citation

Niese, E. (2013). A new recursion for three-column combinatorial Macdonald polynomials. Journal of Combinatorial Theory, Series A, 120(1), 142-158.