Theoretical Foundations of Applied Discrete Mathematics

A characterization of matroids in terms of surfaces

A. V. Il'ev^a, V. P. Il'ev<sup>bc

a</sup> Sobolev Institute of Mathematics, Omsk, Russia
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c Omsk State University, Omsk, Russia

Abstract: 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, surface, rank, combinatorial geometry.

UDC: 519.1+519.151

DOI: 10.17223/20710410/33/1

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