Matroids have been defined in 1935 as generalization of graphs and matrices. Starting from the 1950s they have had increasing interest and the theoretical results obtained have been used for solving several difficult problems in various fields such as civil, electrical, and mechanical engineering, computer science, and mathematics. Oriented matroids are a special class of matroids. They can be viewed as a combinatorial abstraction of real hyperplanes arrangements, of point configurations over the reals, of convex polytopes, or of directed graphs. Scope of this article is to introduce the reader to the theory of oriented matroids, providing an extensive discussion of the axiom systems for them and illustrating the different aspects that characterize these objects.

Oriented matroids

FESTA, PAOLA
2009

Abstract

Matroids have been defined in 1935 as generalization of graphs and matrices. Starting from the 1950s they have had increasing interest and the theoretical results obtained have been used for solving several difficult problems in various fields such as civil, electrical, and mechanical engineering, computer science, and mathematics. Oriented matroids are a special class of matroids. They can be viewed as a combinatorial abstraction of real hyperplanes arrangements, of point configurations over the reals, of convex polytopes, or of directed graphs. Scope of this article is to introduce the reader to the theory of oriented matroids, providing an extensive discussion of the axiom systems for them and illustrating the different aspects that characterize these objects.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/172346
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