{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:25:59Z","timestamp":1759335959661,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A set system is a pair $\\mathcal{S} =\u00a0(V(\\mathcal{S}),\\Delta(\\mathcal{S}))$, where $\\Delta(\\mathcal{S})$ is a family of subsets of the set\u00a0$V(\\mathcal{S})$. We refer to\u00a0the members of $\\Delta(\\mathcal{S})$ as the stable sets of\u00a0$\\mathcal{S}$. A homomorphism between\u00a0two set systems $\\mathcal{S}$ and $\\mathcal{T}$ is a map $f :\u00a0V(\\mathcal{S}) \\rightarrow V(\\mathcal{T})$ such that the preimage under $f$ of every stable set of $\\mathcal{T}$ is a stable set of $\\mathcal{S}$.\u00a0Inspired by a recent generalization due to Engstr\u00f6m of Lov\u00e1sz's Hom complex construction, the author associates a cell complex\u00a0$\\mathrm{Hom}(\\mathcal{S},\\mathcal{T})$ to any two finite\u00a0set 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\u00a0set systems.<\/jats:p>","DOI":"10.37236\/3009","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:00:52Z","timestamp":1578711652000},"source":"Crossref","is-referenced-by-count":3,"title":["Hom Complexes of Set Systems"],"prefix":"10.37236","volume":"20","author":[{"given":"Jakob","family":"Jonsson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p4\/4541","content-type":"application\/zip","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:20:40Z","timestamp":1579299640000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/3009","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,1,7]]},"article-number":"P4"}}