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Simplicial Complexes Obtained from Qualitative Probability Orders

dc.contributor.authorEdelman, Paul H.
dc.contributor.authorGvozdeva, Tatiana
dc.contributor.authorSlinko, A.M. (Arkadii M.)
dc.identifier.citation27 Journal of Discrete Mathematics 1820 (2013)en_US
dc.descriptionarticle published in a peer reviewed, open access journal.en_US
dc.description.abstractThe goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from qualitative probability orders on subsets of a finite set that generalize subset orders induced by probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to refine our understanding of one-point extensions of a particular oriented matroid.en_US
dc.format.extent25 pagesen_US
dc.publisherJournal of Discrete Mathematicsen_US
dc.subjectSimplicial complexesen_US
dc.subjectThreshold complexesen_US
dc.subjectQualitative probability ordersen_US
dc.subjectAcyclic complexesen_US
dc.subject.lcshProbability measuresen_US
dc.subject.lcshCooperative games (Mathematics)en_US
dc.titleSimplicial Complexes Obtained from Qualitative Probability Ordersen_US

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