Matchings for linearly indecomposable modular lattices
type: Item
instance of: scholarly article
title: Matchings for linearly indecomposable modular lattices
zbMATH Open document ID: 0608.06007
DOI: 10.1016/0012-365X(87)90013-6
author: Klaus Reuter
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let L be a finite lattice and let J(L) (M(L), resp.) denote the set of all nonzero join irreducible (all nonunit meet irreducible, resp.) elements of L. The author proves that every finite linearly indecomposable modular lattice L admits a bijection f: J(L)\(\to M(L)\) such that \(x\leq f(x)\) for any \(x\in J(L)\). (A lattice L is called linearly indecomposable if there do not exist x,y\(\in L\) with \(x<y\) such that \(z\leq x\) or \(z\geq y\) for all \(z\in L-\{x,y\}.)\) This result relates to a conjecture by \textit{I. Rival} [Algebra Univers. 6, 303-311 (1976; Zbl 0423.06008)] and complements the theorem of \textit{J. P. S. Kung} [Order 2, 105-112 (1985; Zbl 0582.06008)].
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 3983234
zbMATH Keywords: matching
zbMATH Keywords: join irreducible
zbMATH Keywords: meet irreducible
zbMATH Keywords: finite linearly indecomposable modular lattice
reviewed by: Pavel Pták
MaRDI profile type: Publication
cites work: Proof of a conjecture on finite modular lattices
cites work: Matchings and Radon transforms in lattices. I: Consistent lattices
cites work: Counting formulas for glued lattices
cites work: Combinatorial inequalities for semimodular lattices of breadth two
Wikidata QID: Q126389231
full work available at URL: 0012-365x(87)90013-6
OpenAlex ID: W2026201623
description: scientific article; zbMATH DE number 3983234