Combinatorial Proof of Selberg's Integral Formula
Combinatorics
2020-05-19 v1
Abstract
In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then follows by induction. This solves a problem posed by R. Stanley in 2008. Our proof is based on Andersons analytic proof of the formula. As part of the proof we show a further generalisation of the generalised Vandermonde determinant.
Cite
@article{arxiv.2005.08731,
title = {Combinatorial Proof of Selberg's Integral Formula},
author = {Alexander Haupt},
journal= {arXiv preprint arXiv:2005.08731},
year = {2020}
}