The Selberg integral and Young books
Combinatorics
2014-09-05 v1
Abstract
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.
Cite
@article{arxiv.1409.1317,
title = {The Selberg integral and Young books},
author = {Jang Soo Kim and Suho Oh},
journal= {arXiv preprint arXiv:1409.1317},
year = {2014}
}
Comments
13 pages, 11 figures