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dc.contributor.authorWaldhauser, Tamás
dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
dc.date.accessioned2012-09-26T14:29:48Z
dc.date.available2012-09-26T14:29:48Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10240
dc.language.isoenen
dc.subjectBoolean functionen
dc.subjectpseudo-Boolean functionen
dc.subjectlocal monotonicityen
dc.subjectdiscrete partial derivativeen
dc.subjectjoin and meet derivativesen
dc.subject.ddc512en
dc.titleLocally monotone Boolean and pseudo-Boolean functionsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversity of Szeged;
dc.contributor.editoruniversityotherUniversite du Luxembourg;
dc.description.abstractenWe propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are shown to be tightly related to lattice counterparts of classical partial derivatives via the notion of permutable derivatives. More precisely, p-locally monotone functions are shown to have p-permutable lattice derivatives and, in the case of symmetric functions, these two notions coincide. We provide further results relating these two notions, and present a classification of p-locally monotone functions, as well as of functions having p-permutable derivatives, in terms of certain forbidden “sections”, i.e., functions which can be obtained by substituting constants for variables. This description is made explicit in the special case when p=2.en
dc.relation.isversionofjnlnameDiscrete Applied Mathematics
dc.relation.isversionofjnlvol160en
dc.relation.isversionofjnlissue12en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages1651-1660en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.dam.2012.03.006en
dc.identifier.urlsitehttp://arxiv.org/abs/1107.1161en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAlgèbreen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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