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Article Dans Une Revue European Journal of Combinatorics Année : 2017

First order convergence of matroids

Résumé

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.
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Dates et versions

hal-01416364 , version 1 (14-12-2016)

Identifiants

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František Kardoš, Daniel Král ', Anita Liebenau, Lukáš Mach. First order convergence of matroids. European Journal of Combinatorics, 2017, 59, pp.150 - 168. ⟨10.1016/j.ejc.2016.08.005⟩. ⟨hal-01416364⟩

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