The Cyclic Sieving Phenomenon for Faces of Generalized Cluster Complexes
| dc.creator | Eu, Sen-Peng | |
| dc.creator | Fu, Tung-Shan | |
| dc.date | 2006-12-22 | |
| dc.date.accessioned | 2026-07-07T07:36:50Z | |
| dc.date.available | 2026-07-07T07:36:50Z | |
| dc.description | The notion of cyclic sieving phenomenon is introduced by Reiner, Stanton, and White as a generalization of Stembridge's $q=-1$ phenomenon. The generalized cluster complexes associated to root systems are 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. | |
| dc.description | 26 pages, 14 figures | |
| dc.identifier | https://arxiv.org/abs/math/0612679 | |
| dc.identifier | http://arxiv.org/abs/math/0612679 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120567 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A30 | |
| dc.title | The Cyclic Sieving Phenomenon for Faces of Generalized Cluster Complexes | |
| dc.type | text |