Strong semimodular lattices and Frankl's conjecture
type: Item
instance of: scholarly article
title: Strong semimodular lattices and Frankl's conjecture
zbMATH Open document ID: 1013.06008
author: Tetsuya Abe
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: Frankl's conjecture says that in every nontrivial finite lattice \(L\) there is a join-irreducible element \(a\) such that the principal filter \(F(a)\) has at most \(|L|/2\) elements. It is known that this conjecture holds for lower semimodular or section-complemented lattices, but it is unknown whether it holds for upper semimodular lattices. The author introduces the concept of a strong semimodular lattice and proves Frankl's conjecture for these lattices.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 1899975
zbMATH Keywords: strong semimodular lattice
zbMATH Keywords: Frankl's conjecture
MaRDI profile type: Publication
full work available at URL: s000120050195
OpenAlex ID: W2016384349
Wikidata QID: Q123147395
DOI: 10.1007/S000120050195
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description: scientific article; zbMATH DE number 1899975