On k-antichains in the unit n-cube
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524142" target="_blank" >RIV/67985840:_____/20:00524142 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/20:10422172
Result on the web
<a href="http://dx.doi.org/10.5486/PMD.2020.8787" target="_blank" >http://dx.doi.org/10.5486/PMD.2020.8787</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5486/PMD.2020.8787" target="_blank" >10.5486/PMD.2020.8787</a>
Alternative languages
Result language
angličtina
Original language name
On k-antichains in the unit n-cube
Original language description
A chain in the unit n-cube is a set C ⊂ [0, 1]n such that for every x = (x1, . . . , xn) and y = (y1, . . . , yn) in C, we either have xi ≤ yi for all i ∈ [n], or xi ≥ yi for all i ∈ [n]. We consider subsets A, of the unit n-cube [0, 1]n, that satisfy card(A ∩ C) ≤ k, for all chains C ⊂ [0, 1]n, where k is a fixed positive integer. We refer to such a set A as a k-antichain. We show that the (n − 1)-dimensional Hausdorff measure of a k-antichain in [0, 1]n is at most kn and that the bound is asymptotically sharp. Moreover, we conjecture that there exist k-antichains in [0, 1]n whose (n − 1)-dimensional Hausdorff measure equals kn, and we verify the validity of this conjecture when n = 2.
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ18-01472Y" target="_blank" >GJ18-01472Y: Graph limits and inhomogeneous random graphs</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Publicationes Mathematicae-Debrecen
ISSN
0033-3883
e-ISSN
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Volume of the periodical
96
Issue of the periodical within the volume
3-4
Country of publishing house
HU - HUNGARY
Number of pages
9
Pages from-to
503-511
UT code for WoS article
000530645200015
EID of the result in the Scopus database
2-s2.0-85091172898