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- W3022084233 abstract "Publisher SummaryThis chapter reviews oriented matroids. Matroid theory can be considered as coordinate-free linear algebra, and it has been applied to various fields in mathematics. Radon partitions, supporting hyperplanes, face lattices, Euler's formula, Gale diagrams, Farkas' Lemma from operations research, duality, shellability, the upper bound theorem, and many other well-known concepts in combinatorial convexity have been carried over to and studied within the theory of oriented matroids. The combinatorial part of the theory of convex polytopes can be viewed as part of oriented matroid theory, and the theory of oriented matroids benefits from a well-established theory of convex polytopes. The fact that all matroid polytopes can be generated in a purely combinatorial fashion shows a closure property which the set of ordinary convex polytopes seems to lack. It may be necessary to use different representatives of a given combinatorial type to obtain all the polytopes having one vertex more which are obtainable from polytopes of the given combinatorial type." @default.
- W3022084233 created "2020-05-13" @default.
- W3022084233 creator A5063987912 @default.
- W3022084233 date "1993-01-01" @default.
- W3022084233 modified "2023-09-25" @default.
- W3022084233 title "Oriented Matroids" @default.
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