Carathéodory-type Theorems à la Bárány

Carathéodory-type Theorems à la Bárány,10.1007/s00454-010-9290-z,Discrete & Computational Geometry,Jürgen Bokowski,Javier Bracho,Ricardo Strausz

Carathéodory-type Theorems à la Bárány  
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We generalise the famous Helly–Lovász theorem leading to a generalisation of the Bárány–Carathéodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.
Journal: Discrete & Computational Geometry - DCG , vol. 45, no. 2, pp. 261-271, 2011
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