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Combinatorial proof of Selberg's integral formula
Publikationstyp
Journal Article
Date Issued
2022-01
Sprache
English
Author(s)
Institut
Volume
185
Article Number
105513
Citation
Journal of Combinatorial Theory - Series A 185: 105513 (2022-01)
Publisher DOI
Scopus ID
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.
Subjects
Combinatorial proof
Selberg's integral formula
Sijections
DDC Class
510: Mathematics