COVERING POINTS BY HYPERPLANES AND RELATED PROBLEMS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511352" target="_blank" >RIV/00216208:11320/25:10511352 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bgcSjiXnGT" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bgcSjiXnGT</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/24M1640732" target="_blank" >10.1137/24M1640732</a>

Result language
angličtina
Original language name
COVERING POINTS BY HYPERPLANES AND RELATED PROBLEMS
Original language description
For a set P of n points in R-d, for any d >= 2, a hyperplane h is called k-rich with respect to P if it contains at least k points of P. Answering and generalizing a question asked by Peyman Afshani, we show that if the number of k-rich hyperplanes in R-d, d >= 3, is at least Omega(n(d)/k(alpha) +n/k), with a sufficiently large constant of proportionality and with d <= alpha <2d -1, then there exists a (d -2)-flat that contains Omega(k((2d-1-alpha)/(d-1))) points of P. We also present upper bound constructions that give instances in which the above lower bound is tight. An extension of our analysis yields similar lower bounds for k-rich spheres or k-rich flats.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA25-16847S" target="_blank" >GA25-16847S: Combinatorial structures, continuous mathematics and their impact on the design of efficient algorithms</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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