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Poset limits can be totally ordered
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Hladký, Jan, Máthé, András, Patel, Viresh and Pikhurko, Oleg (2015) Poset limits can be totally ordered. American Mathematical Society. Transactions, 367 (6). pp. 4319-4337. doi:10.1090/S0002-9947-2015-06299-0 ISSN 0002-9947.
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Official URL: https://doi.org/10.1090/S0002-9947-2015-06299-0
Abstract
S. Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529-563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs.
We prove that each poset limit can be represented as a kernel on the unit interval with the standard order, thus answering an open question of Janson. We provide two proofs: real-analytic and combinatorial. The combinatorial proof is based on a Szemerédi-type Regularity Lemma for posets which may be of independent interest.
Also, as a by-product of the analytic proof, we show that every atomless ordered probability space admits a measure-preserving and almost order-preserving map to the unit interval.
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): | Partially ordered sets | ||||
Journal or Publication Title: | American Mathematical Society. Transactions | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 3 February 2015 | ||||
Dates: |
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Volume: | 367 | ||||
Number: | 6 | ||||
Number of Pages: | 19 | ||||
Page Range: | pp. 4319-4337 | ||||
DOI: | 10.1090/S0002-9947-2015-06299-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 6 June 2016 | ||||
Date of first compliant Open Access: | 6 June 2016 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC), National Science Foundation (U.S.) (NSF) | ||||
Grant number: | EP/G050678/1 (ESPRC), EP/J008087/1 (EPSRC), 306493 (ERC), DMS-1100215 (NSF) |
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