DC Field | Value | Language |
---|---|---|
dc.contributor.author | Cheong, Otfried | ko |
dc.contributor.author | Goaoc, Xavier | ko |
dc.contributor.author | Holmsen, Andreas | ko |
dc.date.accessioned | 2013-03-12T04:51:51Z | - |
dc.date.available | 2013-03-12T04:51:51Z | - |
dc.date.created | 2012-09-27 | - |
dc.date.created | 2012-09-27 | - |
dc.date.issued | 2012-08 | - |
dc.identifier.citation | ISRAEL JOURNAL OF MATHEMATICS, v.190, no.1, pp.213 - 228 | - |
dc.identifier.issn | 0021-2172 | - |
dc.identifier.uri | http://hdl.handle.net/10203/101366 | - |
dc.description.abstract | A line l is a transversal to a family F of convex objects in a"e (d) if it intersects every member of F. In this paper we show that for every integer d >= 3 there exists a family of 2d-1 pairwise disjoint unit balls in a"e (d) with the property that every subfamily of size 2d - 2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957. Crucial to the proof is the notion of a pinned transversal, which means an isolated point in the space of transversals. Here we investigate minimal pinning configurations and construct a family F of 2d-1 disjoint unit balls in R-d with the following properties: (i) The space of transversals to F is a single point and (ii) the space of transversals to any proper subfamily of F is a connected set with non-empty interior. | - |
dc.language | English | - |
dc.publisher | HEBREW UNIV MAGNES PRESS | - |
dc.subject | COMMON TRANSVERSALS | - |
dc.subject | UNIT BALLS | - |
dc.subject | THEOREM | - |
dc.subject | CONJECTURE | - |
dc.subject | GRUNBAUM | - |
dc.title | Lower bounds to Helly numbers of line transversals to disjoint congruent balls | - |
dc.type | Article | - |
dc.identifier.wosid | 000307305300010 | - |
dc.identifier.scopusid | 2-s2.0-84863946262 | - |
dc.type.rims | ART | - |
dc.citation.volume | 190 | - |
dc.citation.issue | 1 | - |
dc.citation.beginningpage | 213 | - |
dc.citation.endingpage | 228 | - |
dc.citation.publicationname | ISRAEL JOURNAL OF MATHEMATICS | - |
dc.identifier.doi | 10.1007/s11856-011-0179-1 | - |
dc.contributor.localauthor | Cheong, Otfried | - |
dc.contributor.localauthor | Holmsen, Andreas | - |
dc.contributor.nonIdAuthor | Goaoc, Xavier | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | COMMON TRANSVERSALS | - |
dc.subject.keywordPlus | UNIT BALLS | - |
dc.subject.keywordPlus | THEOREM | - |
dc.subject.keywordPlus | CONJECTURE | - |
dc.subject.keywordPlus | GRUNBAUM | - |
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