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Poset limits can be totally ordered
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SYSNO ASEP 0443353 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Poset limits can be totally ordered Author(s) Hladký, Jan (MU-W) RID, SAI, ORCID
Máthé, A. (GB)
Viresh, P. (GB)
Pikhurko, O. (GB)Source Title American Mathematical Society. Transactions. - : American Mathematical Society - ISSN 0002-9947
Roč. 367, č. 6 (2015), s. 4319-4337Number of pages 19 s. Language eng - English Country US - United States Keywords limits of discrete structures ; regularity lemma ; poset Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000351859600021 EID SCOPUS 84925435048 DOI 10.1090/S0002-9947-2015-06299-0 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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