Lower bound on the size of a quasirandom forcing set of permutations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00125023" target="_blank" >RIV/00216224:14330/22:00125023 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0963548321000298" target="_blank" >http://dx.doi.org/10.1017/S0963548321000298</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0963548321000298" target="_blank" >10.1017/S0963548321000298</a>

Result language
angličtina
Original language name
Lower bound on the size of a quasirandom forcing set of permutations
Original language description
A set S of permutations is forcing if for any sequence {Pi_i} of permutations where the density d(pi, Pi_i) converges to 1/|pi|! for every permutation pi from S, it holds that {Pi_i} is quasirandom. Graham asked whether there exists an integer k such that the set of all permutations of order k is forcing; this has been shown to be true for any k>=4 . In particular, the set of all 24 permutations of order 4 is forcing. We provide the first non-trivial lower bound on the size of a forcing set of permutations: every forcing set of permutations (with arbitrary orders) contains at least four permutations.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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