On the cut-complexes of the 5-cube
type: Item
instance of: scholarly article
title: On the cut-complexes of the 5-cube
zbMATH Open document ID: 0691.52003
DOI: 10.1016/0012-365X(89)90181-7
author: L. Lazarte
author: M. Reza Emamy-K.
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A cut-complex of the d-cube \(c^ d\) is the complex of faces of \(c^ d\) to one side of a hyperplane which cuts it (this is not quite the definition of the paper under review, but does seem to be the actual usage). An exterior edge of a cut-complex C joins a vertex of C to a vertex of the complementary cut-complex, and a cut of \(c^ d\) consists of the exterior edges of some cut-complex. The minimal number of cuts needed to cover the edges of \(c^ d\) is the cut-number \(k(c^ d)\). It is shown here that \(k(c^ 4)=4\); moreover, all general sections of \(c^ 4\) are found. Further, all cut-complexes of \(c^ 5\) are described by implementation of a computer program. Finally, the role of stellar subdivision and its inverse in the construction of a polytope from a simplex are investigated for the sections of \(c^ 4\).
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4131164
zbMATH Keywords: section
zbMATH Keywords: cut-complex
zbMATH Keywords: d-cube
zbMATH Keywords: stellar subdivision
MaRDI profile type: Publication
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full work available at URL: 0012-365x(89)90181-7
OpenAlex ID: W2083407160
description: scientific article; zbMATH DE number 4131164