The complex of maximal lattice free simplices
type: Item
instance of: scholarly article
title: The complex of maximal lattice free simplices
zbMATH Open document ID: 0822.90104
DOI: 10.1007/BF01581150
author: Imre Bárány
author: Herbert Scarf
author: Roger Howe
published in: Mathematical Programming. Series A. Series B
publication date: 1994-10-30T00:00:00Z
review text: A maximal lattice free body is a body of the form \(K= \{x\mid Ax\leq b\}\) containing no lattice points in its interior such that any closed convex body which properly contains \(K\) does have a lattice point in its interior. The simplicial complex \(K(A)\) is defined to be the collection of simplices and their proper subsimplices representing maximal lattice free bodies of the above form with \(A\) a fixed generic \((n+ 1)\times n\)- matrix. The topological space associated with \(K(A)\) is shown to be homeomorphic to \(\mathbb{R}^ n\). The complex \(KZ(A)\) is defined by identifying those simplices or subsimplices of \(K(A)\) which are lattice translates of each other. The associated space is homeomorphic to the \(n\)-torus.
Mathematics Subject Classification ID: 90C10
zbMATH DE Number: 679576
zbMATH Keywords: simplicial complexes
zbMATH Keywords: maximal lattice free body
Wikidata QID: Q101133360
reviewed by: Joachim Piehler
MaRDI profile type: Publication
cites work: Q3884826
cites work: Q4070959
cites work: Production Sets with Indivisibilities, Part I: Generalities
cites work: Production Sets with Indivisibilities, Part II: The Case of Two Activities
cites work: Integral Polyhedra in Three Space
cites work: Neighborhood Systems for Production Sets with Indivisibilities
cites work: Shortest Integer Vectors
full work available at URL: https://doi.org/10.1007/bf01581150
OpenAlex ID: W2074657235
DBLP publication ID: journals/mp/BaranyHS94
description: scientific article; zbMATH DE number 679576