The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen Peng Eu, Tung Shan Fu

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13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)350-376
Number of pages27
JournalAdvances in Applied Mathematics
Volume40
Issue number3
DOIs
Publication statusPublished - 2008 Mar 1

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Keywords

  • Catalan numbers
  • Cluster complex
  • Cyclic sieving phenomenon
  • Dissection

ASJC Scopus subject areas

  • Applied Mathematics

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