dc.contributor.author
Blagojevic, Pavle V. M.
dc.contributor.author
Palic, Nevena
dc.contributor.author
Soberon, Pablo
dc.contributor.author
Ziegler, Günther M.
dc.date.accessioned
2019-11-07T12:56:12Z
dc.date.available
2019-11-07T12:56:12Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/25898
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-25657
dc.description.abstract
Holmsen, Kyncˇl and Valculescu recently conjectured that if a finite set X with in points in Rd that is colored by m different colors can be partitioned into n subsets of i points each, such that each subset contains points of at least d different colors, then there exists such a partition of X with the additional property that the convex hulls of the n subsets are pairwise disjoint.
We prove a continuous analogue of this conjecture, generalized so that each subset contains points of at least c different colors, where we also allow c to be greater than d. Furthermore, we give lower bounds on the fraction of the points each of the subsets contains from c different colors. For example, when n ≤ 2, d ≤ 2, c ≤ d with m ≤ n(c - d) d are integers, and µ1, . . . ,µm are
m positive finite absolutely continuous measures on Rd , we prove that there exists a partition of Rd
into n convex pieces which equiparts the measures µ1, . . . ,µd−1, and in addition every piece of the partition has positive measure with respect to at least c of the measures µ1, . . . ,µm .
2010 Mathematics Subject Classification: 52C35, 51M20 (primary); 55R20, 55N25 (secondary)
en
dc.format.extent
34 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Cutting a part from many measures
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
e37
dcterms.bibliographicCitation.doi
10.1017/fms.2019.33
dcterms.bibliographicCitation.journaltitle
Forum of Mathematics, Sigma
dcterms.bibliographicCitation.volume
7
dcterms.bibliographicCitation.url
https://doi.org/10.1017/fms.2019.33
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
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refubium.funding
Deutsche Forschungsgemeinschaft (DFG)
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin und der DFG gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.issn
2050-5094
dcterms.isPartOf.eissn
2050-5094