TY - JOUR
T1 - The cyclic sieving phenomenon for faces of generalized cluster complexes
AU - Eu, Sen Peng
AU - Fu, Tung Shan
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (S.-P. Eu), [email protected] (T.-S. Fu). 1 S.-P. Eu is partially supported by National Science Council, Taiwan under grant NSC 95-2115-M-390-006-MY3 and TJ & MY Foundation. 2 T.-S. Fu is partially supported by National Science Council, Taiwan under grants NSC 95-2115-M-215-001-MY2 and NSC 96-2918-I-251-002.
PY - 2008/3
Y1 - 2008/3
N2 - 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 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 types An, Bn, Dn, and I2 (a) are shown to exhibit the cyclic sieving phenomenon under a cyclic group action. For the cluster complexes of exceptional types E6, E7, E8, F4, H3, and H4, a verification for such a phenomenon on the facets is given.
AB - 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 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 types An, Bn, Dn, and I2 (a) are shown to exhibit the cyclic sieving phenomenon under a cyclic group action. For the cluster complexes of exceptional types E6, E7, E8, F4, H3, and H4, a verification for such a phenomenon on the facets is given.
KW - Catalan numbers
KW - Cluster complex
KW - Cyclic sieving phenomenon
KW - Dissection
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U2 - 10.1016/j.aam.2007.01.005
DO - 10.1016/j.aam.2007.01.005
M3 - Article
AN - SCOPUS:40649117986
SN - 0196-8858
VL - 40
SP - 350
EP - 376
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
IS - 3
ER -