The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen-Peng Eu, Tung Shan Fu

Research output: Contribution to conferencePaper

Abstract

The notion of cyclic sieving phenomenon was introduced by Reiner, Stanton, and White as a generalization of Stembridge's q = -1 phenomenon. The generalized cluster complexes associated to root systems were given by Fomin and Reading as a generalization of the cluster complexes found by Fomin and Zelevinsky. In this paper, the faces of various dimensions of the generalized cluster complexes in type A n, B n, D n, and I 2(a) are shown to exhibit the cyclic sieving phenomenon under a cyclic group action. For the cluster complexes of exceptional type E 6, E 7, E 8, F 4, H 3, and H 4, a verification for such a phenomenon on their maximal faces is given.

Original languageEnglish
Publication statusPublished - 2007 Dec 1
Event19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China
Duration: 2007 Jul 22007 Jul 6

Other

Other19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
CountryChina
CityTianjin
Period07/7/207/7/6

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Keywords

  • Catalan numbers
  • Cluster complex
  • Cyclic sieving phenomenon
  • Dissection

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Eu, S-P., & Fu, T. S. (2007). The cyclic sieving phenomenon for faces of generalized cluster complexes. Paper presented at 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China.