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Characterization of quasirandom permutations by a pattern sum

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Chan, T., Králʼ, Daniel, Noel, Jonathan A., Pehova, Yanitsa, Sharifzadeh, Maryam and Volec, Jan (2020) Characterization of quasirandom permutations by a pattern sum. Random Structures and Algorithms, 57 (4). pp. 920-939. doi:10.1002/rsa.20956

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Official URL: https://doi.org/10.1002/rsa.20956

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Abstract

It is known that a sequence urn:x-wiley:rsa:media:rsa20956:rsa20956-math-0001 of permutations is quasirandom if and only if the pattern density of every 4‐point permutation in urn:x-wiley:rsa:media:rsa20956:rsa20956-math-0002 converges to 1/24. We show that there is a set S of 4‐point permutations such that the sum of the pattern densities of the permutations from S in the permutations urn:x-wiley:rsa:media:rsa20956:rsa20956-math-0003 converges to urn:x-wiley:rsa:media:rsa20956:rsa20956-math-0004 if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the sets S with this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Permutation groups, Random number generators, Combinatorial analysis
Journal or Publication Title: Random Structures and Algorithms
Publisher: John Wiley & Sons, Inc.
ISSN: 1042-9832
Official Date: December 2020
Dates:
DateEvent
December 2020Published
27 August 2020Available
16 June 2020Accepted
Volume: 57
Number: 4
Page Range: pp. 920-939
DOI: 10.1002/rsa.20956
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: This is the peer reviewed version of the following article: Chan, TFN, Král', D, Noel, JA, Pehova, Y, Sharifzadeh, M, Volec, J. Characterization of quasirandom permutations by a pattern sum. Random Struct Alg. 2020; 1– 20. https://doi.org/10.1002/rsa.20956, which has been published in final form at https://doi.org/10.1002/rsa.20956. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
648509[ERC] Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661
UNSPECIFIEDMasarykova Univerzitahttp://dx.doi.org/10.13039/501100010653
ECF-2018-534Leverhulme Trusthttp://dx.doi.org/10.13039/501100000275
752426[ERC] Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661
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