The cyclic sieving phenomenon for faces of generalized cluster complexes

Sen Peng Eu; Tung Shan Fu

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 conference › Paper › peer-review

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 were 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 their maximal faces is given.

Original language	English
Publication status	Published - 2007
Externally published	Yes
Event	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2007 Jul 2 → 2007 Jul 6

Other

Other	19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/Territory	China
City	Tianjin
Period	2007/07/02 → 2007/07/06

Keywords

Catalan numbers
Cluster complex
Cyclic sieving phenomenon
Dissection

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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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 were 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 their maximal faces 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.; 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 ; Conference date: 02-07-2007 Through 06-07-2007",

year = "2007",

language = "English",

}

TY - CONF

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 - 2007

Y1 - 2007

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 were 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 their maximal faces 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 were 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 their maximal faces is given.

KW - Catalan numbers

KW - Cluster complex

KW - Cyclic sieving phenomenon

KW - Dissection

UR - https://www.scopus.com/pages/publications/84860739157

UR - https://www.scopus.com/pages/publications/84860739157#tab=citedBy

M3 - Paper

AN - SCOPUS:84860739157

T2 - 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07

Y2 - 2 July 2007 through 6 July 2007

ER -

The cyclic sieving phenomenon for faces of generalized cluster complexes

Abstract

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Keywords

ASJC Scopus subject areas

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