Endomorphism semigroups for weak \(p\)-hypergraphs
type: Item
instance of: scholarly article
title: Endomorphism semigroups for weak \(p\)-hypergraphs
zbMATH Open document ID: 0962.20044
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: A hypergraph \((V,E)\) is called a weak \(p\)-hypergraph if it satisfies: (a) for any \(v\in V\) there exists \(A\in E\) with \(v\in A\); (b) \(|A|\geq p+1\) for all \(A\in E\) and for every \(p\)-element subset \(B\subseteq V\) there exists at most one \(A\in E\) with \(B\subseteq A\); (c) there exist \(p+1\) vertices of \(V\) contained in no \(A\in E\). The endomorphism monoids of weak \(p\)-hypergraphs are described by formulas in the elementary theory of semigroups. Two distinct weak \(p\)-hypergraphs have distinct endomorphism monoids and two weak \(p\)-hypergraphs are isomorphic if and only if their endomorphism monoids are isomorphic. Consequences for affine and projective geometries are formulated. The proofs are omitted.
reviewed by: Václav Koubek
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1541587
zbMATH Keywords: endomorphism monoids
zbMATH Keywords: hypergraphs
zbMATH Keywords: affine geometries
zbMATH Keywords: projective geometries
author: Aleksei V. Molchanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541587