An excluded minors method for infinite matroids

Nathan Bowler, Johannes Carmesin

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1 Citation (Scopus)
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Abstract

The notion of thin sums matroids was invented to extend the notion of representability to non-finitary matroids. A matroid is tame if every circuit-cocircuit intersection is finite. We prove that a tame matroid is a thin sums matroid over a finite field k if and only if all its finite minors are representable over k. We expect that the method we use to prove this will make it possible to lift many theorems about finite matroids representable over a finite field to theorems about tame thin sums matroids over these fields. We give three examples of this: various characterisations of binary tame matroids and of regular tame matroids, and unique representability of ternary tame matroids.
Original languageEnglish
Pages (from-to)104-113
JournalJournal of Combinatorial Theory. Series B
Volume128
Early online date24 Aug 2017
DOIs
Publication statusPublished - Jan 2018

Keywords

  • math.CO
  • 05C63, 05B35
  • matroid
  • infinite matroid
  • tree-decomposition
  • representable
  • rot's conjecture
  • minor
  • Tutte-decomposition
  • thin sums
  • ends

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