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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
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: |
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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 | ||||
| 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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