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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 ISSN 1016-443X.
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Official URL: http://dx.doi.org/10.1007/s00039-013-0216-9
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||
Date of first compliant deposit: | 24 December 2015 | ||||
Date of first compliant Open Access: | 24 December 2015 | ||||
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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