Disjoint Unit Spheres Admit At Most Two Line Transversals
Identifieur interne : 003811 ( Crin/Curation ); précédent : 003810; suivant : 003812Disjoint Unit Spheres Admit At Most Two Line Transversals
Auteurs : Otfried Cheong ; Xavier Goaoc ; Hyeon-Suk NaSource :
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Abstract
We show that a set of n disjoint unit spheres in \mathbb{R}^d admits at most two distinct geometric permutations, or line transversals, if n is large enough. This bound is optimal.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="129">Disjoint Unit Spheres Admit At Most Two Line Transversals</title></titleStmt><publicationStmt><idno type="RBID">CRIN:cheong03a</idno><date when="2003" year="2003">2003</date><idno type="wicri:Area/Crin/Corpus">003811</idno><idno type="wicri:Area/Crin/Curation">003811</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Curation">003811</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Disjoint Unit Spheres Admit At Most Two Line Transversals</title><author><name sortKey="Cheong, Otfried" sort="Cheong, Otfried" uniqKey="Cheong O" first="Otfried" last="Cheong">Otfried Cheong</name></author><author><name sortKey="Goaoc, Xavier" sort="Goaoc, Xavier" uniqKey="Goaoc X" first="Xavier" last="Goaoc">Xavier Goaoc</name></author><author><name sortKey="Na, Hyeon Suk" sort="Na, Hyeon Suk" uniqKey="Na H" first="Hyeon-Suk" last="Na">Hyeon-Suk Na</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>computational geometry</term><term>geometric permutation</term><term>transversal</term><term>unit sphere</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="567">We show that a set of n disjoint unit spheres in \mathbb{R}^d admits at most two distinct geometric permutations, or line transversals, if n is large enough. This bound is optimal.</div></front></TEI><BibTex type="inproceedings"><ref>cheong03a</ref><crinnumber>A03-R-071</crinnumber><category>3</category><equipe>Departement of Mathematics and Computer Sciences</equipe><author><e>Cheong, Otfried</e><e>Goaoc, Xavier</e><e>Na, Hyeon-Suk</e></author><title>Disjoint Unit Spheres Admit At Most Two Line Transversals</title><booktitle>{11th Annual European Symposium on Algorithms, Budapest, Hungary}</booktitle><year>2003</year><month>Sep</month><url>http://www.loria.fr/publications/2003/A03-R-071/A03-R-071.ps</url><keywords><e>geometric permutation</e><e>transversal</e><e>unit sphere</e><e>computational geometry</e></keywords><abstract>We show that a set of n disjoint unit spheres in \mathbb{R}^d admits at most two distinct geometric permutations, or line transversals, if n is large enough. This bound is optimal.</abstract></BibTex></record>Pour manipuler ce document sous Unix (Dilib)
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