Tableaux and plane partitions of truncated shapes

被引：15

作者：

Panova, Greta ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2012年 / 49卷 / 3-5期

关键词：

Truncated shapes; Young tableaux; Plane partitions; Hook-length formulas; Schur functions;

D O I：

10.1016/j.aam.2012.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a new kind of straight and shifted plane partitions/Young tableaux - ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function. (c) 2012 Elsevier Inc. All rights reserved.

引用

页码：196 / 217

页数：22