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dc.contributor.authorŽivaljević, Radeen
dc.contributor.authorVrećica, Sinišaen
dc.date.accessioned2020-04-12T18:04:00Z-
dc.date.available2020-04-12T18:04:00Z-
dc.date.issued1992-01-01en
dc.identifier.issn0097-3165en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/314-
dc.description.abstractLet t, r, and d be positive integers and let C1, C2, ..., Cd+1 be a collection of (d + 1) disjoint sets in Rd, called colors, each of cardinality at least t. If S = {a1, a2, ..., ad+1} is a subset of A {colon equals} ∪i=1d+1 Ci, then both S and the, possibly degenerate, simplex conv S is called multicolored if S ∩ Ci ≠ {circled division slash} for all 1 ≤ i ≤ d + 1. Let T(r, d) denotes the smallest value t such that for every collection of "colors" {Ci | 1 ≤ i ≤ d + 1}, |Ci| ≥ t, there exist r disjoint, multicolored sets Si, i = 1, ..., r, such that ∩i=1r conv(Si) ≠ {circled division slash}. It is proved that T(r, d) ≤ 4r-1 for all r and T(r, d) ≤ 2r - 1 for all primes r. This estimate answers a question from (Bárány et al., in "Proceedings, 5th Annual Sympos. Comput. Geom., 1989," pp. 140-144) and at the same time provides a missing link of the proof that the number hd(n) of halving hyperplanes for a set of n points in Rd satisfies the inequality hd(n) ≤ O(nd-ε) for some ε > 0.en
dc.publisherElsevier-
dc.relation.ispartofJournal of Combinatorial Theory, Series Aen
dc.titleThe colored Tverberg's problem and complexes of injective functionsen
dc.typeArticleen
dc.identifier.doi10.1016/0097-3165(92)90028-Sen
dc.identifier.scopus2-s2.0-0007135945en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage309en
dc.relation.lastpage318en
dc.relation.issue2en
dc.relation.volume61en
dc.description.rankM21-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0001-9801-8839-
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