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dc.contributor.authorde Longueville, Marken
dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:58Z-
dc.date.available2020-04-12T18:03:58Z-
dc.date.issued2008-06-20en
dc.identifier.issn0001-8708en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/298-
dc.description.abstractThe well-known "splitting necklace theorem" of Alon [N. Alon, Splitting necklaces, Adv. Math. 63 (1987) 247-253] says that each necklace with k ṡ ai beads of color i = 1, ..., n, can be fairly divided between k thieves by at most n (k - 1) cuts. Alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace [0, 1] where beads of given color are interpreted as measurable sets Ai ⊂ [0, 1] (or more generally as continuous measures μi). We demonstrate that Alon's result is a special case of a multidimensional consensus division theorem about n continuous probability measures μ1, ..., μn on a d-cube [0, 1]d. The dissection is performed by m1 + ⋯ + md = n (k - 1) hyperplanes parallel to the sides of [0, 1]d dividing the cube into m1 ṡ ⋯ ṡ md elementary cuboids (parallelepipeds) where the integers mi are prescribed in advance.en
dc.publisherElsevier-
dc.relation.ispartofAdvances in Mathematicsen
dc.subjectAlon's splitting necklace theorem | Consensus division | Equivariant maps | Topological shellabilityen
dc.titleSplitting multidimensional necklacesen
dc.typeArticleen
dc.identifier.doi10.1016/j.aim.2008.02.003en
dc.identifier.scopus2-s2.0-41949120385en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage926en
dc.relation.lastpage939en
dc.relation.issue3en
dc.relation.volume218en
dc.description.rankM21a-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0001-9801-8839-
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