Lines in the Manhattan Plane
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438558" target="_blank" >RIV/00216208:11320/21:10438558 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-83823-2_133" target="_blank" >https://doi.org/10.1007/978-3-030-83823-2_133</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-83823-2_133" target="_blank" >10.1007/978-3-030-83823-2_133</a>
Alternative languages
Result language
angličtina
Original language name
Lines in the Manhattan Plane
Original language description
A well-known theorem in plane geometry states that any set of n non-collinear points in the plane determines at least n lines. Chen and Chvátal asked whether an analogous statement holds within the framework of finite metric spaces, with lines defined using the notion of betweenness. In this paper, we prove that in the plane with the L1 (also called Manhattan) metric, a non-collinear set induces at least LEFT CEILING n/ 2 RIGHT CEILING lines. This is an improvement of the previous lower bound of n/37, with substantially different proof.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GJ19-04113Y" target="_blank" >GJ19-04113Y: Advanced tools in combinatorics, topology and related areas</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Trends in Mathematics
ISBN
978-3-030-83823-2
ISSN
2297-0215
e-ISSN
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Number of pages
7
Pages from-to
835-841
Publisher name
Springer Nature
Place of publication
Neuveden
Event location
Barcelona
Event date
Sep 6, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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