The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen Peng Eu; Tung Shan Fu

doi:10.1016/j.aam.2007.01.005

The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen Peng Eu^*
, Tung Shan Fu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 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 A_n, B_n, D_n, 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 language	English
Pages (from-to)	350-376
Number of pages	27
Journal	Advances in Applied Mathematics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2007.01.005
Publication status	Published - 2008 Mar
Externally published	Yes

Keywords

Catalan numbers
Cluster complex
Cyclic sieving phenomenon
Dissection

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2007.01.005

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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\}",

note = "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.",

year = "2008",

month = mar,

doi = "10.1016/j.aam.2007.01.005",

language = "English",

volume = "40",

pages = "350--376",

journal = "Advances in Applied Mathematics",

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publisher = "Academic Press Inc.",

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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

UR - https://www.scopus.com/pages/publications/40649117986

UR - https://www.scopus.com/pages/publications/40649117986#tab=citedBy

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 -

The cyclic sieving phenomenon for faces of generalized cluster complexes

Abstract

Keywords

ASJC Scopus subject areas

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