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Oriented matroids and multiply ordered sets

โœ Scribed by Jim Lawrence


Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
795 KB
Volume
48
Category
Article
ISSN
0024-3795

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Matroids on Partially Ordered Sets
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## L dimension may be chosen within each of the subspaces L in the set S that are ''in general position.'' For example, in the real projective space of dimension 3, consider a plane , a line r not belonging to , the point P [ r l , and two distinct points Q, R both different from P, lying on the l

Oriented Matroids and Hyperplane Transve
โœ Laura Anderson; Rephael Wenger ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 401 KB

We prove that a finite family A of compact connected sets in R d has a hyperplane transversal if and only if for some k, 0<k<d, there exists an acyclic oriented matroid of rank k+1 on A such that every k+2 sets in A have an oriented k-transversal which meets the sets consistently with that oriented

Cyclic Polytopes and Oriented Matroids
โœ Raul Cordovil; Pierre Duchet ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 244 KB

Consider the moment curve in the real euclidean space R d defined parametrically by the map ฮณ : R โ†’ R d , t โ†’ ฮณ (t) = (t, t 2 , . . . , t d ). The cyclic d-polytope C d (t 1 , . . . , t n ) is the convex hull of n > d different points on this curve. The matroidal analogs are the alternating oriented

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โœ Raul Cordovil; Komei Fukuda ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 240 KB

An oriented matroid lattice is a lattice arising from the span of cocircuits of an oriented matroid ordered by conformal relation. One important subclass of the o.m. lattices is the polars of face lattices of zonotopes. In this paper we show that every o.m. lattice is a (combinatorial) manifold. Thi

Antipodal graphs and oriented matroids
โœ Komei Fukuda; Keiichi Handa ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 786 KB

A graph is antipodal if, for every vertex c', there exists exactly one vertex V which is not closer to r than every vertex adjacent to 6. In this paper we consider the problem of characterizing tope graphs of oriented matroids, which constitute a broad class of antipodal graphs. One of the results i