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

Fingerprint

Face
Root System
Cyclic group
Group Action
Generalization

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.

The cyclic sieving phenomenon for faces of generalized cluster complexes. / Eu, Sen-Peng; Fu, Tung Shan.

2007. Paper presented at 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China.

Research output: Contribution to conferencePaper

Eu, S-P & Fu, TS 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, 07/7/2 - 07/7/6, .
Eu S-P, Fu TS. The cyclic sieving phenomenon for faces of generalized cluster complexes. 2007. Paper presented at 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China.
Eu, Sen-Peng ; Fu, Tung Shan. / 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.
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