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On Some Classes of Linear Representable Matroids

In: Formal Power Series and Algebraic Combinatorics

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  • A. M. Revyakin

    (Moscow State University)

Abstract

The starting point of the theory of matroids goes back to the thirties of our century when B. L. van der Waerden ([1, 7]) considered, in his “Modern algebra”, not only linear dependence but the algebraic dependence as well, and H. Whitney [23], in his attempt to generalize the notion of dual graph, defined for the first time the notion of matroid. Later, M. Mclane proposed an interpretation of matroid in terms of projective geometry (that was the reason to call matroids combinatorial geometries), and G. Birkhoff [2] defined the notion of M-structure (matroid lattice) and proved that projective geometries are such structures. This paper gives characterizations of some classes of liner representable matroids.

Suggested Citation

  • A. M. Revyakin, 2000. "On Some Classes of Linear Representable Matroids," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 564-574, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_54
    DOI: 10.1007/978-3-662-04166-6_54
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