Hom complexes of set systems
type: Item
instance of: scholarly article
title: Hom complexes of set systems
zbMATH Open document ID: 1267.05303
author: Jakob Jonsson
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v20i1p4
review text: Summary: A set system is a pair \(\mathcal{S}\) = (\(V(\mathcal{S}),\Delta(\mathcal{S})\)), where \(\Delta(\mathcal{S})\) is a family of subsets of the set \(V(\mathcal{S})\). We refer to the members of \(\Delta(\mathcal{S})\) as the stable sets of \(\mathcal{S}\). A homomorphism between two set systems \(\mathcal{S}\) and \(\mathcal{T}\) is a map \(f : V(\mathcal{S}) \rightarrow V(\mathcal{T})\) such that the preimage under \(f\) of every stable set of \(\mathcal{T}\) is a stable set of \(\mathcal{S}\). Inspired by a recent generalization due to Engström of Lovász's Hom complex construction, the author associates a cell complex \(\operatorname{Hom}(\mathcal{S},\mathcal{T})\) to any two finite set systems \(\mathcal{S}\) and \(\mathcal{T}\). The main goal of the paper is to examine basic topological and homological properties of this cell complex for various pairs of set systems.
Mathematics Subject Classification ID: 05E45
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 55S35
zbMATH DE Number: 6171843
zbMATH Keywords: Hom complex
zbMATH Keywords: set system
zbMATH Keywords: partitionable poset
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171843