How small can a lattice of order-dimension n be?
type: Item
instance of: scholarly article
title: How small can a lattice of order-dimension n be?
zbMATH Open document ID: 0614.06005
DOI: 10.1007/BF00340776
author: Yanyan Li
published in: Order
publication date: 1987-01-01T00:00:00Z
review text: This paper is concerned with the dimension of two particular classes of lattices, namely partition lattices and linear lattices. The main motivation was provided by the following question: For a lattice L, does dim L\(=n\) always imply \(| L| \geq 2^ n?\) The answer is in the negative. Indeed, suitable lower bounds are established on the dimension of both partition and linear lattices that show that from some n on both classes of lattices fail to obey the bound \(2^ n\). - In the case of partition lattices, the dimension is determined up to an absolute constant. For \(L_ n\), the linear lattice over GF(2), the authors succeed in determining the dimension up to a factor C/n for an absolute constant C.
reviewed by: S.Gacsályi
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 3993649
zbMATH Keywords: order-dimension
zbMATH Keywords: Ferrers relation
zbMATH Keywords: partition lattices
zbMATH Keywords: linear lattices
MaRDI profile type: Publication
cites work: On the dimension of partially ordered sets
cites work: Q3964626
cites work: Q3952147
cites work: Q4071247
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description: scientific article; zbMATH DE number 3993649