Cutset condition for geometric lattices
type: Item
instance of: scholarly article
title: Cutset condition for geometric lattices
zbMATH Open document ID: 1118.06003
author: Jun Wang
author: Jun Wu
published in: Order
publication date: 2007-04-26T00:00:00Z
review text: Let \(L\) be a lattice with bottom \(0\) and top \(1\), \(a, b \in L\), \(aMb\) will denote that \((a,b)\) is a modular pair. If \(aMx\) and \(xMa\) holds for any \(x\in L\), then \(a\) is called a modular element. If a subset \(C\) of \(L\) meets every maximal chain, then \(C\) is called a cutset of \(L\). The modular cutset condition requires that there exists a cutset \(C\) of modular elements such that \(0\not\in C, 1 \not\in C\). The authors continue their work on cutsets and geometric lattices. Their main result is: If an atomistic lattice \(L\) of finite length fulfils the modular cutset condition, then \(L\) is semimodular.
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 5146177
zbMATH Keywords: atomistic lattice
zbMATH Keywords: geometric lattice, semimodular lattice of finite length
zbMATH Keywords: modular pair
zbMATH Keywords: modular element
zbMATH Keywords: cutset
reviewed by: Horst Szambien
MaRDI profile type: Publication
full work available at URL: s11083-006-9051-z
OpenAlex ID: W2071173708
cites work: Q5532570
cites work: Left-modular elements of lattices
cites work: Q5623714
cites work: Modular elements of geometric lattices
cites work: Q4256200
DOI: 10.1007/S11083-006-9051-Z
description: scientific article; zbMATH DE number 5146177