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First order convergence of matroids
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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
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Official URL: http://dx.doi.org/10.1016/j.ejc.2016.08.005
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 | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| 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: |
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| 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 | ||||||||||
| 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) | ||||||||||
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