Rectangular products of lattices
type: Item
instance of: scholarly article
title: Rectangular products of lattices
zbMATH Open document ID: 0693.06006
DOI: 10.1016/0012-365X(90)90332-C
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The author discusses the properties which are preserved or not preserved in rectangular products \(L_ 1\square L_ 2\) of given lattices \(L_ 1\) and \(L_ 2\). If \(L_ 1\) and \(L_ 2\) are face lattices then \(L_ 1\square L_ 2\) is the lattice of faces of the (topological) product of these polytopes. If \(L_ 1\) and \(L_ 2\) are concept lattices in the sense of Wille, then \(L_ 1\square L_ 2\) is the concept lattice of the semiproduct of the underlying contexts. The author gives necessary and sufficient conditions for a lattice to be a rectangular product.
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 06C20
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4134109
zbMATH Keywords: face lattices
zbMATH Keywords: polytopes
zbMATH Keywords: concept lattices
zbMATH Keywords: contexts
zbMATH Keywords: rectangular product
author: Mary Katherine Bennett
MaRDI profile type: Publication
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full work available at URL: 0012-365x(90)90332-c
OpenAlex ID: W2072279465
description: scientific article; zbMATH DE number 4134109