Kardos, Frantisek, Králʼ, Daniel, Liebenau, Anita and Mach, Lukáš (2017) First order convergence of matroids. European Journal of Combinatorics, 59 . pp. 150-168. doi:10.1016/j.ejc.2016.08.005 ISSN 0195-6698.

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Abstract

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini–Schramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this result: every first order convergent sequence of matroids with bounded branch-depth representable over a fixed finite field has a limit modeling, i.e., there exists an infinite matroid with the elements forming a probability space that has asymptotically the same first order properties. We show that neither of the bounded branch-depth assumption nor the representability assumption can be removed.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Matroids, Convergence, Combinatorial analysis
Journal or Publication Title:	European Journal of Combinatorics
Publisher:	Academic Press
ISSN:	0195-6698
Official Date:	January 2017
Dates:	Date Event January 2017 Published 7 September 2016 Available 13 August 2016 Accepted 26 January 2015 Submitted
Volume:	59
Page Range:	pp. 150-168
DOI:	10.1016/j.ejc.2016.08.005
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	15 August 2016
Date of first compliant Open Access:	7 September 2017
Funder:	Seventh Framework Programme (European Commission) (FP7), Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	Grant agreement no. 259385 (FP7), EP/M025365/1 (EPSRC)
Related URLs:	Publisher

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