Combinatorial analogs of Brouwer's fixed-point theorem on a bounded polyhedron
type: Item
instance of: scholarly article
title: Combinatorial analogs of Brouwer's fixed-point theorem on a bounded polyhedron
zbMATH Open document ID: 0723.55001
DOI: 10.1016/0095-8956(89)90020-8
author: Robert M. Freund
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: This paper presents a combinatorial theorem (Theorem 1) on a bounded polyhedron for an unrestricted labelling of a triangulation of the polyhedron, which can be interpreted as an extension of the generalized Sperner lemma. When the labelling function is dual-proper, this theorem specializes to a second combinatorial theorem on the polyhedron, that is an extension of Scarf's dual Sperner lemma. These results are shown to be analogs of Brouwer's fixed-point theorem on a polyhedron, and are also shown to generalize other combinatorial theorems on bounded polyhedra. As part of the combinatorial proof of theorem 1, a pseudomanifold construction for a polyhedron and its dual are also presented.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 4192641
zbMATH Keywords: bounded polyhedron
zbMATH Keywords: Sperner lemma
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: pseudomanifold
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90020-8
OpenAlex ID: W1974855372
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description: scientific article; zbMATH DE number 4192641