Universal arrays

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00547093" target="_blank" >RIV/67985807:_____/21:00547093 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.disc.2021.112626" target="_blank" >http://dx.doi.org/10.1016/j.disc.2021.112626</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2021.112626" target="_blank" >10.1016/j.disc.2021.112626</a>

Result language
angličtina
Original language name
Universal arrays
Original language description
A word on q symbols is a sequence of letters from a fixed alphabet of size q. For an integer k⩾1, we say that a word w is k-universal if, given an arbitrary word of length k, one can obtain it by removing letters from w. It is easily seen that the minimum length of a k-universal word on q symbols is exactly qk. We prove that almost every word of size (1+o(1))cqk is k-universal with high probability, where c q is an explicit constant whose value is roughly q log⁡ q. Moreover, we show that the k-universality property for uniformly chosen words exhibits a sharp threshold. Finally, by extending techniques of Alon (2017) [1], we give asymptotically tight bounds for every higher dimensional analogue of this problem.
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
10101 - Pure mathematics

Project
<a href="/en/project/GA19-08740S" target="_blank" >GA19-08740S: Embedding, Packing and Limits in Graphs</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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