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The structure of 2-separations of infinite matroids

2012/01/05 by Elad Aigner‐Horev, Elad Aigner-Horev, Reinhard Diestel +4
Computer Science · Mathematics · #05 #Advanced Algebra and Logic #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #math.CO #msc:05

paper · pdf · doi:10.48550/arxiv.1201.1135

31 pages

openalex publication_date 2012/01/05 · arxiv created 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalizing a well known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits, and the edges of T correspond to certain nested 2-separations of M. These decompositions are invariant under duality.

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