The extension to root systems of a theorem on tournaments
type: Item
instance of: scholarly article
title: The extension to root systems of a theorem on tournaments
zbMATH Open document ID: 0595.05038
DOI: 10.1016/0097-3165(86)90082-8
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: Kendall and Smith proved that if a tournament p' is obtained from a tournament p by reversing the edges of a 3-cycle then p and p' contain the same number of 3-cycles. This result is the basis of cancellation argument used by Zeilberger and Bressoud in their proof of the q-analog of Dyson's conjecture which may be stated in terms of the root system \(A_ n\). The main result of this paper is the extension to arbitrary root systems. As an application of a combinatorial proof of a special case of the Macdonald's conjecture is given for root systems using the method of Zeilberger and Bressoud. Another application is a combinatorial proof of Weyl's denominator formula.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3957146
zbMATH Keywords: tournament
zbMATH Keywords: 3-cycles
zbMATH Keywords: Dyson's conjecture
zbMATH Keywords: root systems
zbMATH Keywords: Macdonald's conjecture
zbMATH Keywords: Weyl's denominator formula
author: Robert Calderbank
author: Philip J. Hanlon
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90082-8
OpenAlex ID: W2008540304
cites work: Colored tournaments and Weyl's denominator formula
cites work: Tournaments and Vandermond's determinant
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cites work: The orders of the finite Chevalley groups
cites work: A proof of Andrews' \(q\)-Dyson conjecture
description: scientific article; zbMATH DE number 3957146