The number of unit distances is almost linear for most norms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10100315" target="_blank" >RIV/00216208:11320/11:10100315 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2010.09.009" target="_blank" >http://dx.doi.org/10.1016/j.aim.2010.09.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2010.09.009" target="_blank" >10.1016/j.aim.2010.09.009</a>
Alternative languages
Result language
angličtina
Original language name
The number of unit distances is almost linear for most norms
Original language description
We prove that there exists a norm in the plane under which no n-point set determines more than O(n log n loglog n) unit distances. Actually, most norms have this property, in the sense that their complement is a meager set in the metric space of all norms (with the metric given by the Hausdorff distance of the unit balls).
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
—
Volume of the periodical
226
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
2618-2628
UT code for WoS article
000286159100014
EID of the result in the Scopus database
—