Lines in the Plane with the L1 Metric

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455858" target="_blank" >RIV/00216208:11320/22:10455858 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cDi5EmTJ_J" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cDi5EmTJ_J</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-022-00443-3" target="_blank" >10.1007/s00454-022-00443-3</a>

Result language
angličtina
Original language name
Lines in the Plane with the L1 Metric
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 of n points 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. As a consequence, we also get the same lower bound for non-collinear point sets in the plane with the Loo metric.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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)

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)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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