Math @ Duke

Publications [#236008] of Robert Calderbank
Papers Published
 Calderbank, AR; Hanlon, P, The extension to root systems of a theorem on tournaments,
Journal of Combinatorial Theory, Series A, vol. 41 no. 2
(1986),
pp. 228245, ISSN 00973165
(last updated on 2018/10/17)
Abstract: M. G. Kendall and B. BabingtonSmith proved that if a tournament p′ is obtained from a tournament p by reversing the edges of a 3cycle then p and p′ contain the same number of 3cycles. This theorem is the basis of a cancellation argument used by D. Zeilberer and D. M. Bressoud in their recent proof of the qanalog 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.


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