Questions tagged [oriented-matroids]
Hyperplane arrangements, discrete geometry, convex polytopes, and optimization. For more general questions concerning matroids, use the matroid-theory tag.
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questions with no upvoted or accepted answers
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How many components are there in the space of "generic" planar N-gons? (Mnev's revenge)
Call an ordered $N$-tuple of points in the Euclidean plane ${\mathbb R} ^2$ "in general position" if no three points of the points in the set are collinear. As a function of $N$ how many components ...
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Is every planar point set the projection of vertices of a neighborly 4-polytope?
More exactly, written in coordinates, I'm curious to know if for every point set $(x_i,y_i)$ there are $(x_i,y_i,z_i,w_i)$ that are vertices of a neighborly polytope.
This problem comes from a simple ...
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Matroid Representation of the Antichains of a Poset
Introduction
I am studying a problem in which the antichains of a poset are of key importance. They are naturally geometrically embedded as vectors in the space $\mathbb{R}^P$, where $P$ is the poset,...
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Every triangulation of an oriented matroid is partitionable
In his unpublished article, Combinatorial properties of triangulations of oriented matroids, Julian Webster proves that every triangulation of an oriented matroid is partitionable.
Does this result ...
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Will the following construction leads to an counterexample of strong mapping conjecture on realizable oriented matroids?
The strong map conjecture asserts that any strong map $\mathcal{M}_1\rightarrow\mathcal{M}_2$ admit a factorization into an extension followed by a contraction. For which the counterexample has been ...
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Enumerate all possible sign patterns spanned by matrix column space
Given a $m \times n$ matrix $A$ with $m>n$, I would like to enumerate all possible sign patterns $w$ generated by $Av$ for all $v \in \mathbb{R}^n$. More specifically, if $(Av)_i \geq 0$ then $w_i =...
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What are / could be the applications of Delaunay oriented matroids?
The Delaunay oriented matroid is studied in detail by F. Santos (actually this paper is more general).
For a set of points $S$ (in any dimension), let $C$ be a sphere, $C^+$ be its interior, $C^-$ be ...