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.
|出版狀態||已發佈 - 2007 十二月 1|
|事件||19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, 中国|
持續時間: 2007 七月 2 → 2007 七月 6
|其他||19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07|
|期間||07/7/2 → 07/7/6|
ASJC Scopus subject areas
- Algebra and Number Theory