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Quasirandom permutations are characterized by 4-point densities

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Král’, Daniel and Pikhurko, Oleg (2013) Quasirandom permutations are characterized by 4-point densities. Geometric and Functional Analysis, Volume 23 (Number 2). pp. 570-579. doi:10.1007/s00039-013-0216-9

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Official URL: http://dx.doi.org/10.1007/s00039-013-0216-9

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Abstract

For permutations π and τ of lengths |π|≤|τ| , let t(π,τ) be the probability that the restriction of τ to a random |π| -point set is (order) isomorphic to π . We show that every sequence {τj} of permutations such that |τj|→∞ and t(π,τj)→1/4! for every 4-point permutation π is quasirandom (that is, t(π,τj)→1/|π|! for every π ). This answers a question posed by Graham.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Permutations, Density functionals
Journal or Publication Title: Geometric and Functional Analysis
Publisher: Birkhaeuser Verlag AG
ISSN: 1016-443X
Official Date: April 2013
Dates:
DateEvent
April 2013Published
Volume: Volume 23
Number: Number 2
Page Range: pp. 570-579
DOI: 10.1007/s00039-013-0216-9
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: European Research Council (ERC), Seventh Framework Programme (European Commission) (FP7), National Science Foundation (U.S.) (NSF)
Grant number: 259385 (ERC), 306493 (ERC), DMS-1100215 (NSF)

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