The extension to root systems of a theorem on tournaments
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.
scientific article; zbMATH DE number 3957146