Cutting polytopes and flag \(f\)-vectors
type: Item
instance of: scholarly article
title: Cutting polytopes and flag \(f\)-vectors
zbMATH Open document ID: 0956.52012
DOI: 10.1007/PL00009499
author: Yanyan Li
published in: Discrete \& Computational Geometry
publication date: 2000-03-23T00:00:00Z
review text: The \({\mathbf c}{\mathbf d}\)-index of a polytope \(P\) encodes all the entries of the flag \(f\)-vector of \(P\). However, even standard operations on polytopes, such as the join and direct product, lead to complicated expressions for the resulting \({\mathbf c}{\mathbf d}\)-indices. Here, the authors show how to find the \({\mathbf c}{\mathbf d}\)-index of the polytope obtained by cutting off a face \(F\) of \(P\), by which is meant moving a hyperplane which supports \(P\) in \(F\) a little into \(P\). On the way, they find the \({\mathbf c}{\mathbf d}\)-index of the cell complex obtained by contracting \(F\) to a point.
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 1422802
zbMATH Keywords: cutting polytope
zbMATH Keywords: contracting face
zbMATH Keywords: \({\mathbf c}{\mathbf d}\)-index
zbMATH Keywords: flag \(f\)-vector
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: pl00009499
OpenAlex ID: W2155851113
Recommended article: Flag vectors of multiplicial polytopes
Recommended article: On the cut polytope
Recommended article: On polytopes cut by flats
Recommended article: Q4036750
Recommended article: The cut polytope and the Boolean quadric polytope
Recommended article: Facet-reducing cuts of a convex polytope
Recommended article: Q4851806
Recommended article: Relationships among flag \(f\)-vector inequalities for polytopes
Recommended article: Q3391324
Recommended article: On the polyhedral structure of uniform cut polytopes
description: scientific article; zbMATH DE number 1422802