A proof of the q,t-square conjecture

被引：9

作者：

Can, Mahir ^{[1
]}

Loehr, Nicholas

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2006年 / 113卷 / 07期

关键词：

square lattice paths; Catalan numbers; Bergeron-Garsia nabla operator; plethysm; Macdonald polynomials;

D O I：

10.1016/j.jcta.2006.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a combinatorial formula conjectured by Loehr and Warrington for the coefficient of the sign character in del(p(n)). Here del denotes the Bergeron-Garsia nabla operator, and p is a power-sum symmetric function. The combinatorial formula enumerates lattice paths in an n x n square according to two suitable statistics. (c) 2006 Elsevier Inc. All rights reserved.

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页码：1419 / 1434

页数：16

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