The cyclic sieving phenomenon for faces of cyclic polytopes
type: Item
instance of: scholarly article
title: The cyclic sieving phenomenon for faces of cyclic polytopes
zbMATH Open document ID: 1225.05019
author: Sen-Peng Eu
author: Tung-Shan Fu
author: Yeh-Jong Pan
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/228038
full work available at URL: v17i1r47.html
review text: Summary: A cyclic polytope of dimension \(d\) with \(n\) vertices is a convex polytope combinatorially equivalent to the convex hull of \(n\) distinct points on a moment curve in \({\mathbb{R}}^d\). 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.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 52B15
zbMATH DE Number: 5721441
zbMATH Keywords: odd-dimensional cyclic polytopes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721441