Axioms for infinite matroids

@article{Bruhn2010AxiomsFI,
  title={Axioms for infinite matroids},
  author={Henning Bruhn and Reinhard Diestel and Matthias Kriesell and Rudi Pendavingh and Paul Wollan},
  journal={Advances in Mathematics},
  year={2010},
  volume={239},
  pages={18-46}
}
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References

SHOWING 1-10 OF 66 REFERENCES
Thin sums matroids and duality
Finite connectivity in infinite matroids
Duality theory for finite and infinite matroids with coefficients
Decomposition of regular matroids
Strong Duality Property for Matroids with Coefficients
TLDR
This paper characterize those Klee matroids arising as closure operators of matroid with coefficients that have the strong duality property and studies the subclass corresponding to the case in which both dualities coincide.
Submodular Functions, Matroids, and Certain Polyhedra
  • J. Edmonds
  • Mathematics
    Combinatorial Optimization
  • 2001
The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the…
Infinite matroids in graphs
Recent work in matroid representation theory
Equicardinality of bases in $B$-matroids
It is very well known that any two bases of a finitary matroid (see [2] for definitions) have the same cardinality. As Dlab has shown in [1], the same does not hold for arbitrary transitive exchange…
Infinite matroid union
We consider the problem of determining whether the union of two infinite matroids is a matroid. We introduce a superclass of the finitary matroids, the nearly finitary matroids, and prove that the…
...
1
2
3
4
5
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