Document Type
Article
Publication Date
1-2013
Abstract
The Hilbert series of the Garsia–Haiman module Mμ 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!).
Recommended Citation
Niese, E. (2013). A new recursion for three-column combinatorial Macdonald polynomials. Journal of Combinatorial Theory, Series A, 120(1), 142-158.
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.
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