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On the intersection conjecture for infinite trees of matroids
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- 2021
Relative rank axioms for infinite matroids
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- 2010
In a recent paper, Bruhn, Diestel, Kriesell and Wollan (arXiv:1003.3919) present four systems of axioms for infinite matroids, in terms of independent sets, bases, closure and circuits. No system of…
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We generalise the construction of infinite matroids from trees of matroids to allow the matroids at the nodes, as well as the field over which they are represented, to be infinite.
Factorization theorems for strong maps between matroids of arbitrary cardinality
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- 2016
Abstract In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps…
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This paper investigates infinite matroids from a categorical perspective. We prove that the category of infinite matroids is a proto-exact category in the sense of Dyckerhoff and Kapranov, thereby…
The Almost Intersection Property for Pairs of Matroids on Common Groundset
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It is proved that if a pair satisfies the Almost Intersection Property then it satisfies the Matroid Intersection Conjecture of Nash-Williams and some corollaries of that result are presented.
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