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arXiv · 1606.04235

Reconstruction of infinite matroids from their 3-connected minors

Nathan Bowler·Johannes Carmesin·Luke Postle
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Abstract

We show that any infinite matroid can be reconstructed from the torsos of a tree-decomposition over its 2-separations, together with local information at the ends of the tree. We show that if the matroid is tame then this local information is simply a choice of whether circuits are permitted to use that end. The same is true if each torso is planar, with all gluing elements on a common face.

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Nathan Bowler, Johannes Carmesin, Luke Postle. 2016-06-14. Reconstruction of infinite matroids from their 3-connected minors. https://arxiv.org/abs/1606.04235

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