The cyclic sieving phenomenon for faces of cyclic polytopes

Sen Peng Eu, Tung Shan Fu, Yeh Jong Pan

Research output: Contribution to journalArticlepeer-review

Abstract

A cyclic polytope of dimension d with n vertices is a convex polytope combinato- rially equivalent to the convex hull of n distinct points on a moment curve in Rd. In this paper, we prove the cyclic sieving phenomenon, introduced by Reiner-Stanton-White, for faces of an even-dimensional cyclic polytope, under a group action that cyclically translates the vertices. For odd-dimensional cyclic polytopes, we enumerate the faces that are invariant under an automorphism that reverses the order of the vertices and an automorphism that interchanges the two end vertices, according to the order on the curve. In particular, for n = d + 2, we give instances of the phenomenon under the groups that cyclically translate the odd-positioned and even-positioned vertices, respectively.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
DOIs
Publication statusPublished - 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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