The extension to root systems of a theorem on tournaments


Journal Article

M. G. Kendall and B. Babington-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 theorem is the basis of a cancellation argument used by D. Zeilberer and D. M. Bressoud in their recent proof of the q-analog of Dyson's conjecture. The theorem may be restated in terms of the root system An and the main result of this paper is the extension of this theorem to arbitrary root systems. As one application we give a combinatorial proof of a special case of the Macdonald conjecture for root systems using the method of Zeilberger and Bressoud. A second application is a combinatorial proof of the Weyl denominator formula. © 1986.

Full Text

Duke Authors

Cited Authors

  • Calderbank, AR; Hanlon, P

Published Date

  • January 1, 1986

Published In

Volume / Issue

  • 41 / 2

Start / End Page

  • 228 - 245

Electronic International Standard Serial Number (EISSN)

  • 1096-0899

International Standard Serial Number (ISSN)

  • 0097-3165

Digital Object Identifier (DOI)

  • 10.1016/0097-3165(86)90082-8

Citation Source

  • Scopus