Chains of modular elements and lattice connectivity
type: Item
instance of: scholarly article
title: Chains of modular elements and lattice connectivity
zbMATH Open document ID: 1118.06002
author: Patricia Hersh
author: John Shareshian
published in: Order
publication date: 2007-04-26T00:00:00Z
review text: It is well-known that if a finite lattice \(L\) possesses a maximal chain \(0<m_1<m_2<\cdots<m_r<1\) in which all elements \(m_i\), \( i=1,2,\dots,r\), are modular, then its order complex is at least \((r-2)\)-connected. The goal of the present note is to generalize the above result. Its main theorem (Theorem 1) shows that the conclusion remains valid without the assumption that the considered chain is maximal.
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06A11
Mathematics Subject Classification ID: 05E25
zbMATH DE Number: 5146179
zbMATH Keywords: lattice
zbMATH Keywords: modular element
zbMATH Keywords: topological connectivity
zbMATH Keywords: order complex
reviewed by: Marius Tărnăuceanu
MaRDI profile type: Publication
full work available at URL: s11083-006-9053-x
OpenAlex ID: W2050224042
cites work: Shellable and Cohen-Macaulay Partially Ordered Sets
cites work: Q4324358
cites work: Q4871782
cites work: A homotopy complementation formula for partially ordered sets
cites work: The lcm-lattice in monomial resolutions
cites work: The Koszul property in affine semigroup rings
cites work: Q5701859
cites work: Combinatorial Commutative Algebra
cites work: Resolutions and lattices
cites work: How to shell a monoid
cites work: Subgroup lattices of groups
cites work: Supersolvable lattices
cites work: Homotopy types of subspace arrangements via diagrams of spaces
DOI: 10.1007/S11083-006-9053-X
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description: scientific article; zbMATH DE number 5146179