The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen Peng Eu, Tung Shan Fu

Research output: Contribution to journalArticle

12 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

Fingerprint

Face
Root System
Cyclic group
Group Action
Facet
Generalization

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

The cyclic sieving phenomenon for faces of generalized cluster complexes. / Eu, Sen Peng; Fu, Tung Shan.

In: Advances in Applied Mathematics, Vol. 40, No. 3, 01.03.2008, p. 350-376.

Research output: Contribution to journalArticle

@article{04f22c0eebbe4f66b9f7a9e9b2df92d2,
title = "The cyclic sieving phenomenon for faces of generalized cluster complexes",
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.",
keywords = "Catalan numbers, Cluster complex, Cyclic sieving phenomenon, Dissection",
author = "Eu, {Sen Peng} and Fu, {Tung Shan}",
year = "2008",
month = "3",
day = "1",
doi = "10.1016/j.aam.2007.01.005",
language = "English",
volume = "40",
pages = "350--376",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - The cyclic sieving phenomenon for faces of generalized cluster complexes

AU - Eu, Sen Peng

AU - Fu, Tung Shan

PY - 2008/3/1

Y1 - 2008/3/1

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

UR - http://www.scopus.com/inward/record.url?scp=40649117986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=40649117986&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2007.01.005

DO - 10.1016/j.aam.2007.01.005

M3 - Article

AN - SCOPUS:40649117986

VL - 40

SP - 350

EP - 376

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

IS - 3

ER -