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Results tagged with convex-geometry
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user 15187
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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Centrally symmetric neighborly polytopes
Let $P$ be a centrally symmetric $k$-neighborly $d$-polytope. Let $ P^* $ is polar (also dual) of $P$. Consider a polytope $Q^*$ , $Q^* \subset P^* $(not necessarily a face of $P^*$). By duality,
$P …
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faces of a polytope
Let $a_1,a_2,..,a_n\in\mathbb{R}^m$, $n>m$ and the points are in general position meaning, no hyperplane contains more than $m$ points. Define a polyhedron $$P=\{x\in\mathbb{R}^m:a_1'x\leq0, a_2'x\l …
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