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dc.contributor.authorIronmonger, Victoria Louise
dc.contributor.authorRuskuc, Nik
dc.date.accessioned2024-02-21T16:30:15Z
dc.date.available2024-02-21T16:30:15Z
dc.date.issued2024-02-14
dc.identifier298462043
dc.identifier0ff8b5fd-6cfe-4212-93da-b90a6a913ea0
dc.identifier85185116499
dc.identifier.citationIronmonger , V L & Ruskuc , N 2024 , ' Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings ' , Order . https://doi.org/10.1007/s11083-024-09659-9en
dc.identifier.issn0167-8094
dc.identifier.otherORCID: /0000-0003-2415-9334/work/153977339
dc.identifier.urihttps://hdl.handle.net/10023/29315
dc.description.abstractWe consider the posets of equivalence relations on finite sets under the standard embedding ordering and under the consecutive embedding ordering. In the latter case, the relations are also assumed to have an underlying linear order, which governs consecutive embeddings. For each poset we ask the well quasi-order and atomicity decidability questions: Given finitely many equivalence relations ρ1,...,ρk, is the downward closed set Av(ρ1,...,ρk) consisting of all equivalence relations which do not contain any of ρ1,...,ρk (a) well-quasi-ordered, meaning that it contains no infinite antichains? and (b) atomic, meaning that it is not a union of two proper downward closed subsets, or, equivalently, that it satisfies the joint embedding property?
dc.format.extent26
dc.format.extent727794
dc.language.isoeng
dc.relation.ispartofOrderen
dc.subjectEquivalence relationen
dc.subjectEmbeddingen
dc.subjectPoseten
dc.subjectWell quasi-orderen
dc.subjectAntichainen
dc.subjectAtomicen
dc.subjectJoint embedding propertyen
dc.subjectGraphen
dc.subjectPathen
dc.subjectSubpathen
dc.subjectDecidabilityen
dc.subjectQA Mathematicsen
dc.subjectT-DASen
dc.subject.lccQAen
dc.titleDecidability of well quasi-order and atomicity for equivalence relations under embedding orderingsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1007/s11083-024-09659-9
dc.description.statusPeer revieweden
dc.identifier.urlhttps://arxiv.org/abs/2301.11048en


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