The Cyclic Sieving Phenomenon for Faces of Generalized Cluster Complexes
Authors: Sen-Peng Eu and Tung-Shan Fu
ABSTRACT
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 the
facets is given.
DIMACS Home Page