On Helly numbers of exponential lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10473475" target="_blank" >RIV/00216208:11320/24:10473475 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Fv-TRXpkE_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Fv-TRXpkE_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2023.103884" target="_blank" >10.1016/j.ejc.2023.103884</a>

Result language
angličtina
Original language name
On Helly numbers of exponential lattices
Original language description
Given a set S subset of R-2, define the Helly number of S, denoted by H(S), as the smallest positive integer N, if it exists, for which the following statement is true: for any finite family F of convex sets in R(2 )such that the intersection of any N or fewer members of F contains at least one point of S, there is a point of S common to all members of F.We prove that the Helly numbers of exponential lattices {alpha(n): n is an element of N-0}(2) are finite for every alpha > 1 and we deter-mine their exact values in some instances. In particular, we obtain H({2(n): n is an element of N-0}(2)) = 5, solving a problem posed by Dillon (2021).For real numbers alpha, beta > 1, we also fully characterize exponential lattices L(alpha, beta) = {alpha(n) : n is an element of N-0} x {beta(n) : n is an element of N-0} with finite Helly numbers by showing that H(L(alpha, beta)) is finite if and only if log(alpha)(beta) is rational.(c) 2023 Elsevier Ltd. All rights reserved.
Czech name
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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/GA21-32817S" target="_blank" >GA21-32817S: Algorithmic, structural and complexity aspects of geometric configurations</a><br>
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

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