Geodesic
A characterization of matroids in terms of surfaces
Prikladnaâ diskretnaâ matematika, no. 3 (2016), pp. 5-15.

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In the paper, the matroids of finite rank and finite-dimensional combinatorial geometries are studied. A definition of a matroid in terms of different rank surfaces satisfying some incidence axioms is proposed. This definition is equivalent to the definition of a matroid in terms of independent sets. In case of a simple matroid its characterization can be viewed as an equivalent definition of a combinatorial geometry.
Keywords: matroid, rank, combinatorial geometry.
Mots-clés : surface 
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A. V. Il'ev; V. P. Il'ev. A characterization of matroids in terms of surfaces. Prikladnaâ diskretnaâ matematika, no. 3 (2016), pp. 5-15. http://geodesic.mathdoc.fr/item/PDM_2016_3_a0/

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