Poset limits can be totally ordered

0443353 - MÚ 2016 RIV US eng J - Journal Article
Hladký, Jan - Máthé, A. - Viresh, P. - Pikhurko, O.
Poset limits can be totally ordered.
American Mathematical Society. Transactions. Roč. 367, č. 6 (2015), s. 4319-4337. ISSN 0002-9947. E-ISSN 1088-6850
Institutional support: RVO:67985840
Keywords : limits of discrete structures * regularity lemma * poset
Subject RIV: BA - General Mathematics
Impact factor: 1.196, year: 2015
http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06299-0/home.html

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.
Permanent Link: http://hdl.handle.net/11104/0246083