article

The cyclic sieving phenomenon

Authors:

D. WhiteAuthors Info & Claims

Journal of Combinatorial Theory Series A, Volume 108, Issue 1

Pages 17 - 50

https://doi.org/10.1016/j.jcta.2004.04.009

Published: 01 October 2004 Publication History

Abstract

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

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Cited By

Bernstein JStriker JVorland C(2024) P-strict promotion and Q-partition rowmotionEuropean Journal of Combinatorics10.1016/j.ejc.2023.103776115:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.ejc.2023.103776
Oh J(2022)Macdonald polynomials and cyclic sievingEuropean Journal of Combinatorics10.1016/j.ejc.2021.103465101:COnline publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1016/j.ejc.2021.103465
Oh YPark E(2021) q-dimensions of highest weight crystals and cyclic sieving phenomenonEuropean Journal of Combinatorics10.1016/j.ejc.2021.10337297:COnline publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1016/j.ejc.2021.103372
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Index Terms

The cyclic sieving phenomenon
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Permutations and combinations
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Journal of Combinatorial Theory Series A

Journal of Combinatorial Theory Series A Volume 108, Issue 1

October 2004

163 pages

ISSN:0097-3165

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Academic Press, Inc.

United States

Publication History

Published: 01 October 2004

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Cited By

Bernstein JStriker JVorland C(2024) P-strict promotion and Q-partition rowmotionEuropean Journal of Combinatorics10.1016/j.ejc.2023.103776115:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.ejc.2023.103776
Oh J(2022)Macdonald polynomials and cyclic sievingEuropean Journal of Combinatorics10.1016/j.ejc.2021.103465101:COnline publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1016/j.ejc.2021.103465
Oh YPark E(2021) q-dimensions of highest weight crystals and cyclic sieving phenomenonEuropean Journal of Combinatorics10.1016/j.ejc.2021.10337297:COnline publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1016/j.ejc.2021.103372
Ahlbach C(2021)Tableau stabilization and rectangular tableaux fixed by promotion powersJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-020-00955-253:4(1057-1116)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s10801-020-00955-2
Billey SKonvalinka MSwanson J(2020)Asymptotic normality of the major index on standard tableauxAdvances in Applied Mathematics10.1016/j.aam.2019.101972113:COnline publication date: 1-Feb-2020
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Patrias R(2019)Promotion on generalized oscillating tableaux and web rotationJournal of Combinatorial Theory Series A10.1016/j.jcta.2018.07.005161:C(1-28)Online publication date: 1-Jan-2019
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Alexandersson PAmini N(2019)The cone of cyclic sieving phenomenaDiscrete Mathematics10.1016/j.disc.2019.01.037342:6(1581-1601)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1016/j.disc.2019.01.037
Mandel HPechenik O(2018)Orbits of plane partitions of exceptional Lie typeEuropean Journal of Combinatorics10.1016/j.ejc.2018.07.00774:C(90-109)Online publication date: 1-Dec-2018
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Ahlbach CSwanson J(2018)Refined cyclic sieving on words for the major index statisticEuropean Journal of Combinatorics10.1016/j.ejc.2018.05.00373:C(37-60)Online publication date: 1-Oct-2018
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Dilks KPechenik OStriker J(2017)Resonance in orbits of plane partitions and increasing tableauxJournal of Combinatorial Theory Series A10.1016/j.jcta.2016.12.007148:C(244-274)Online publication date: 1-May-2017
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