On Some Classes of Linear Representable Matroids

A. M. Revyakin
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A. M. Revyakin: Moscow State University

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 564-574 from Springer

Abstract: 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.

Keywords: Projective Geometry; Dual Graph; Combinatorial Geometry; Unimodular Matrix; Binary Matroids (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_54

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DOI: 10.1007/978-3-662-04166-6_54

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