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Axioms for infinite matroids
"... We give axiomatic foundations for nonfinitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a problem of Rado of 1966. ..."
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Cited by 18 (5 self)
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We give axiomatic foundations for nonfinitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a problem of Rado of 1966.
Infinite Matroids and Determinacy of Games
, 2013
"... Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the WellquasiorderingConjecture to infinite matroids and to show that the class of planar infinite matroids does not have a univer ..."
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Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the WellquasiorderingConjecture to infinite matroids and to show that the class of planar infinite matroids does not have a universal matroid. The existence of these matroids has a connection to Set Theory in that it corresponds to the Determinacy of certain games. To show that our construction gives matroids, we introduce a new very simple axiomatization of the class of countable tame matroids.
The ubiquity of Psimatroids
, 2014
"... Solving (for tame matroids) a problem of AignerHorev, Diestel and Postle, we prove that every tame matroid M can be reconstructed from its canonical tree decomposition into 3connected pieces, circuits and cocircuits together with information about which ends of the decomposition tree are used by ..."
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Solving (for tame matroids) a problem of AignerHorev, Diestel and Postle, we prove that every tame matroid M can be reconstructed from its canonical tree decomposition into 3connected pieces, circuits and cocircuits together with information about which ends of the decomposition tree are used by M. For every locally finite graph G, we show that every tame matroid whose circuits are topological circles of G and whose cocircuits are bonds of G is determined by the set Ψ of ends it uses, that is, it is a Ψmatroid. 1
Infinite graphic matroids  Part I
, 2014
"... An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graphlike topological space: that is, a graphlike space in the sense of Thomassen and ..."
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An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graphlike topological space: that is, a graphlike space in the sense of Thomassen and Vella. This extends Tutte’s characterization of finite graphic matroids. The representation we construct has many pleasant topological properties. Working in the representing space, we prove that any circuit in a 3connected graphic matroid is countable.