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arXiv · 1409.1317

The Selberg integral and Young books

Jang Soo Kim·Suho Oh
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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.

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Jang Soo Kim, Suho Oh. 2014-09-04. The Selberg integral and Young books. https://arxiv.org/abs/1409.1317

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