Publisher DOI: 10.1016/j.jcta.2021.105513
Title: Combinatorial proof of Selberg's integral formula
Language: English
Authors: Haupt, Alexander  
Keywords: Combinatorial proof; Selberg's integral formula; Sijections
Issue Date: Jan-2022
Source: Journal of Combinatorial Theory. Series A 185: 105513 (2022-01)
Abstract (english): 
In this paper we present a combinatorial proof of Selberg's integral formula. We prove a theorem about the number of topological orderings of a certain related directed graph bijectively. Selberg's integral formula then follows by induction. This solves a problem posed by R. Stanley in 2009. Our proof is based on Anderson's analytic proof of the formula. As part of the proof we show a further generalisation of the generalised Vandermonde determinant.
ISSN: 0097-3165
Journal: Journal of combinatorial theory - Series A 
Institute: Mathematik E-10 
Document Type: Article
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