Characterization of quasirandom permutations by a pattern sum

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00118500" target="_blank" >RIV/00216224:14330/20:00118500 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/rsa.20956" target="_blank" >http://dx.doi.org/10.1002/rsa.20956</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/rsa.20956" target="_blank" >10.1002/rsa.20956</a>

Result language
angličtina
Original language name
Characterization of quasirandom permutations by a pattern sum
Original language description
It is known that a sequence{pi i}i is an element of Nof permutations is quasirandom if and only if the pattern density of every 4-point permutation in pi iconverges to 1/24. We show that there is a setSof 4-point permutations such that the sum of the pattern densities of the permutations fromSin the permutations pi iconverges to|S|/24if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the setsSwith this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight.
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
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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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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