A new recursion for three-column combinatorial Macdonald polynomials

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Niese, Elizabeth

关键词: Symmetric functions;    Tableaux;    Macdonald polynomials;   

DOI  :  10.1016/j.jcta.2012.07.008

来源: Elsevier

【 摘 要 】

The Hilbert series (F) over tilde (mu) of the Garsia-Haiman module M-mu can be described combinatorially as the generating function of certain fillings of the Ferrers diagram of mu where mu is an integer partition of n. Since there are n! fillings that generate (F) over tilde (mu), it is desirable to find recursions to reduce the number of fillings that need to be considered when computing (F) over tilde (mu) combinatorially. In this paper, we present a combinatorial recursion for the case where mu is an n by 3 rectangle. This allows us to reduce the number of fillings under consideration from (3n)! to (3n)!/(3!(n)n!). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free