Metric spaces in which many triangles are degenerate

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10484944" target="_blank" >RIV/00216208:11320/24:10484944 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ayy5r0Y6u5" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ayy5r0Y6u5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2024.02.021" target="_blank" >10.1016/j.dam.2024.02.021</a>

Result language
angličtina
Original language name
Metric spaces in which many triangles are degenerate
Original language description
Richmond and Richmond (1997) proved the following theorem: If, in a metric space with at least five points, all triangles are degenerate, then the space is isometric to a subset of the real line. We prove that the hypothesis is unnecessarily strong: In a metric space on n points, fewer than 7n2/6 suitably placed degenerate triangles suffice. However, fewer than n(n - 1)/2 degenerate triangles, no matter how cleverly placed, never suffice. (c) 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)