The Selberg integral and Young books

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:145

Article

Kim, Jang Soo¹  Oh, Suho² 

[1] Sungkyunkwan Univ, Dept Math, Suwon, South Korea

[2] Texas State Univ, Dept Math, San Marcos, TX USA

关键词: Selberg integral;    Standard Young tableau;    Product formula;    Truncated shape;   

DOI  :  10.1016/j.jcta.2016.07.005

来源: Elsevier

【 摘 要 】

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects Young books are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, product formulas for the number of standard Young tableaux of these shapes are obtained. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free