DC Field | Value | Language |
---|---|---|
dc.contributor.author | Holmsen, Andreas | ko |
dc.contributor.author | Roldan-Pensado, Edgardo | ko |
dc.date.accessioned | 2016-10-07T09:31:44Z | - |
dc.date.available | 2016-10-07T09:31:44Z | - |
dc.date.created | 2015-02-02 | - |
dc.date.created | 2015-02-02 | - |
dc.date.issued | 2016-08 | - |
dc.identifier.citation | COMBINATORICA, v.36, no.4, pp.417 - 429 | - |
dc.identifier.issn | 0209-9683 | - |
dc.identifier.uri | http://hdl.handle.net/10203/213262 | - |
dc.description.abstract | Hadwiger's transversal theorem gives necessary and suffcient conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtained by Goodman, Pollack and Wenger, and recently a colorful version appeared due to Arocha, Bracho and Montejano. We show that it is possible to combine both results to obtain a colored version of Hadwiger's theorem in higher dimensions. The proofs differ from the previous ones and use a variant of the Borsuk-Ulam theorem. To be precise, we prove the following. Let F be a family of convex sets in a"e (d) in bijection with a set P of points in a"e (d-1). Assume that there is a coloring of F with suffciently many colors such that any colorful Radon partition of points in P corresponds to a colorful Radon partition of sets in F. Then some monochromatic subfamily of F has a hyperplane transversal. | - |
dc.language | English | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.title | The colored Hadwiger transversal theorem in a"e (d) | - |
dc.type | Article | - |
dc.identifier.wosid | 000382389800003 | - |
dc.identifier.scopusid | 2-s2.0-84930023311 | - |
dc.type.rims | ART | - |
dc.citation.volume | 36 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 417 | - |
dc.citation.endingpage | 429 | - |
dc.citation.publicationname | COMBINATORICA | - |
dc.identifier.doi | 10.1007/s00493-014-3192-2 | - |
dc.contributor.localauthor | Holmsen, Andreas | - |
dc.contributor.nonIdAuthor | Roldan-Pensado, Edgardo | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | SETS | - |
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