The cyclic sieving phenomenon

V. Reiner; D. Stanton; D. White

doi:10.1016/j.jcta.2004.04.009

The cyclic sieving phenomenon

V. Reiner, D. Stanton, D. White

School of Mathematics

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

163 Scopus citations

Abstract

The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q=-1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues.

Original language	English (US)
Pages (from-to)	17-50
Number of pages	34
Journal	Journal of Combinatorial Theory. Series A
Volume	108
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2004.04.009
State	Published - Oct 2004

Keywords

Hook formula
Kraskiewicz-Weyman
Noncrossing partitions
Ordered tree
Polygon dissections
Principal specialization
Roots-of-unity
Schur function
Singer cycle
Springer regular element
q-Binomial coefficient
q-Multinomial coefficient

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10.1016/j.jcta.2004.04.009

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title = "The cyclic sieving phenomenon",

abstract = "The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q=-1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, P{\'o}lya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues.",

keywords = "Hook formula, Kraskiewicz-Weyman, Noncrossing partitions, Ordered tree, Polygon dissections, Principal specialization, Roots-of-unity, Schur function, Singer cycle, Springer regular element, q-Binomial coefficient, q-Multinomial coefficient",

author = "V. Reiner and D. Stanton and D. White",

year = "2004",

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doi = "10.1016/j.jcta.2004.04.009",

language = "English (US)",

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T1 - The cyclic sieving phenomenon

AU - Reiner, V.

AU - Stanton, D.

AU - White, D.

PY - 2004/10

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N2 - The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q=-1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues.

AB - The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q=-1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues.

KW - Hook formula

KW - Kraskiewicz-Weyman

KW - Noncrossing partitions

KW - Ordered tree

KW - Polygon dissections

KW - Principal specialization

KW - Roots-of-unity

KW - Schur function

KW - Singer cycle

KW - Springer regular element

KW - q-Binomial coefficient

KW - q-Multinomial coefficient

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DO - 10.1016/j.jcta.2004.04.009

M3 - Article

AN - SCOPUS:9244260155

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SP - 17

EP - 50

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -

The cyclic sieving phenomenon

Abstract

Keywords

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