Variants of the RSK algorithm adapted to combinatorial Macdonald polynomials

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:146

Article

Loehr, Nicholas A.^1,2 

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] US Naval Acad, Dept Math, Annapolis, MD 21402 USA

关键词: RSK algorithm;    Robinson-Schensted correspondence;    Macdonald polynomials;    Schur polynomials;    Permutation statistics;   

DOI  :  10.1016/j.jcta.2016.09.002

来源: Elsevier

【 摘 要 】

We introduce variations of the Robinson-Schensted correspondence parametrized by positive integers p. Each variation gives a bijection between permutations and pairs of standard tableaux of the same shape. In addition to sharing many of the properties of the classical Schensted algorithm, the new algorithms are designed to be compatible with certain permutation statistics introduced by Haglund in the study of Macdonald polynomials. In particular, these algorithms provide an elementary bijective proof converting Haglund's combinatorial formula for Macdonald polynomials to an explicit combinatorial Schur expansion of Macdonald polynomials indexed by partitions mu, satisfying mu(1) <= 3 and mu(2) <= 2. We challenge the research community to extend this RSK-based approach to more general classes of partitions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free