About: A lower bound on the size of Lipschitz subsets in dimension 3

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We prove: Any n-point set in R^3 has a subset of substantially more than n^{1/2} points 3-Lipschitz in some coordinate. A set S is C-Lipschitz in the z-coordinate if \|z(a)-z(b)\| < C max(\|x(a)-x(b)\|,\|y(a)-y(b)\|) for every a,b in S. We prove: Any n-point set in R^3 has a subset of substantially more than n^{1/2} points 3-Lipschitz in some coordinate. A set S is C-Lipschitz in the z-coordinate if \|z(a)-z(b)\| < C max(\|x(a)-x(b)\|,\|y(a)-y(b)\|) for every a,b in S. (en)
Title	A lower bound on the size of Lipschitz subsets in dimension 3 A lower bound on the size of Lipschitz subsets in dimension 3 (en)
skos:prefLabel	A lower bound on the size of Lipschitz subsets in dimension 3 A lower bound on the size of Lipschitz subsets in dimension 3 (en)
skos:notation	RIV/00216208:11320/03:00002629!RIV/2004/MSM/113204/N
http://linked.open.../vavai/riv/strany	427;430
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LN00A056), Z(MSM 113200005)
http://linked.open...iv/cisloPeriodika	-
http://linked.open...vai/riv/dodaniDat	2004
http://linked.open...aciTvurceVysledku	Matoušek, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	596928
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/03:00002629
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	lower;bound;Lipschitz;subsets;dimension;3 (en)
http://linked.open.../riv/klicoveSlovo	bound Lipschitz lower dimension subsets 3
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[ED8CB2FD5D13]
http://linked.open...i/riv/nazevZdroje	Combinatorics Probability and Computing
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute of Theoretical Computer Science (Center of Young Science)
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	12
http://linked.open...iv/tvurceVysledku	Matoušek, Jiří
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20113200005
issn	0963-5483
number of pages	4 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

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