|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.
|URI:||http://hdl.handle.net/11420/10264||ISSN:||0097-3165||Journal:||Journal of combinatorial theory - Series A||Institute:||Mathematik E-10||Document Type:||Article|
|Appears in Collections:||Publications without fulltext|
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