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- Oriented_matroid abstract "An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces). In comparison, an ordinary (i.e., non-oriented) matroid abstracts the dependence properties that are common both to graphs, which are not necessarily directed, and to arrangements of vectors over fields, which are not necessarily ordered.All oriented matroids have an underlying matroid. Thus, results on ordinary matroids can be applied to oriented matroids. However, the converse is false; some matroids cannot become an oriented matroid by orienting an underlying structure (e.g., circuits or independent sets).The distinction between matroids and oriented matroids is discussed further below.Matroids are often useful in areas such as dimension theory and algorithms.Because of an oriented matroid's inclusion of additional details about the oriented nature of a structure,its usefulness extends further into several areas including geometry and optimization.".
- Oriented_matroid thumbnail Max-flow_min-cut_example.svg?width=300.
- Oriented_matroid wikiPageExternalLink fukuda1982thesis.pdf.
- Oriented_matroid wikiPageExternalLink ~terlaky.
- Oriented_matroid wikiPageExternalLink publications.
- Oriented_matroid wikiPageExternalLink dut-twi-96-103.ps.gz.
- Oriented_matroid wikiPageExternalLink ~fukuda.
- Oriented_matroid wikiPageExternalLink publ.html.
- Oriented_matroid wikiPageID "24338041".
- Oriented_matroid wikiPageRevisionID "601336275".
- Oriented_matroid hasPhotoCollection Oriented_matroid.
- Oriented_matroid subject Category:Oriented_matroids.
- Oriented_matroid comment "An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces).".
- Oriented_matroid label "Oriented matroid".
- Oriented_matroid sameAs m.07s3s_s.
- Oriented_matroid sameAs Q16155113.
- Oriented_matroid sameAs Q16155113.
- Oriented_matroid wasDerivedFrom Oriented_matroid?oldid=601336275.
- Oriented_matroid depiction Max-flow_min-cut_example.svg.
- Oriented_matroid isPrimaryTopicOf Oriented_matroid.
