The cyclic sieving phenomenon

V. Reiner, D. Stanton, D. White

Research output: Contribution to journalArticlepeer-review

121 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 languageEnglish (US)
Pages (from-to)17-50
Number of pages34
JournalJournal of Combinatorial Theory. Series A
Volume108
Issue number1
DOIs
StatePublished - 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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