The minimal k-dispersion of point sets in high dimensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00327961" target="_blank" >RIV/68407700:21340/19:00327961 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jco.2018.10.001" target="_blank" >https://doi.org/10.1016/j.jco.2018.10.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jco.2018.10.001" target="_blank" >10.1016/j.jco.2018.10.001</a>

Result language
angličtina
Original language name
The minimal k-dispersion of point sets in high dimensions
Original language description
In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set P_n={x_1,...,x_n}subset [0,1]^d and kin{0,...,n}, we define the k-dispersion to be the volume of the largest box amidst a point set containing at most k points. The minimal k-dispersion is then given by the infimum over all possible point sets of cardinality n. We provide both upper and lower bounds for the minimal k-dispersion that coincide with the known bounds for the classical minimal dispersion for a surprisingly large range of k’s.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-00580S" target="_blank" >GA18-00580S: Function Spaces and Approximation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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