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|
|事件||19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, 中国|
持續時間: 2007 7月 2 → 2007 7月 6
|其他||19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07|
|期間||2007/07/02 → 2007/07/06|
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