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The extension to root systems of a theorem on tournaments

Publication ,  Journal Article
Calderbank, AR; Hanlon, P
Published in: Journal of Combinatorial Theory, Series A
January 1, 1986

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.

Duke Scholars

Published In

Journal of Combinatorial Theory, Series A

DOI

EISSN

1096-0899

ISSN

0097-3165

Publication Date

January 1, 1986

Volume

41

Issue

2

Start / End Page

228 / 245

Related Subject Headings

  • Computation Theory & Mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
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Calderbank, A. R., & Hanlon, P. (1986). The extension to root systems of a theorem on tournaments. Journal of Combinatorial Theory, Series A, 41(2), 228–245. https://doi.org/10.1016/0097-3165(86)90082-8
Calderbank, A. R., and P. Hanlon. “The extension to root systems of a theorem on tournaments.” Journal of Combinatorial Theory, Series A 41, no. 2 (January 1, 1986): 228–45. https://doi.org/10.1016/0097-3165(86)90082-8.
Calderbank AR, Hanlon P. The extension to root systems of a theorem on tournaments. Journal of Combinatorial Theory, Series A. 1986 Jan 1;41(2):228–45.
Calderbank, A. R., and P. Hanlon. “The extension to root systems of a theorem on tournaments.” Journal of Combinatorial Theory, Series A, vol. 41, no. 2, Jan. 1986, pp. 228–45. Scopus, doi:10.1016/0097-3165(86)90082-8.
Calderbank AR, Hanlon P. The extension to root systems of a theorem on tournaments. Journal of Combinatorial Theory, Series A. 1986 Jan 1;41(2):228–245.
Journal cover image

Published In

Journal of Combinatorial Theory, Series A

DOI

EISSN

1096-0899

ISSN

0097-3165

Publication Date

January 1, 1986

Volume

41

Issue

2

Start / End Page

228 / 245

Related Subject Headings

  • Computation Theory & Mathematics
  • 0101 Pure Mathematics