The cyclic sieving phenomenon for faces of cyclic polytopes

Sen Peng Eu*, Tung Shan Fu, Yeh Jong Pan


研究成果: 雜誌貢獻期刊論文同行評審


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.

頁(從 - 到)1-17
期刊Electronic Journal of Combinatorics
出版狀態已發佈 - 2010

ASJC Scopus subject areas

  • 理論電腦科學
  • 幾何和拓撲
  • 離散數學和組合
  • 計算機理論與數學
  • 應用數學


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