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On the intersection of infinite matroids. (English) Zbl 1384.05061

Summary: We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by R. Aharoni and E. Berger [Invent. Math. 176, No. 1, 1–62 (2009; Zbl 1216.05092)].
We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids.
In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05C63 Infinite graphs
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)

Citations:

Zbl 1216.05092
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References:

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