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Polytopes

  • Corrado De Concini
  • Claudio Procesi
Chapter
Part of the Universitext book series (UTX)

Abstract

Our basic datum is a list X := (a1, …, am) of nonzero elements in a real s-dimensional vector space V (we allow repetitions in the list, since this is important for the applications). Sometimes we take \(V = \mathbb{R}^{s}\) and then think of the ai as the columns of an \(s \times m\)matrix A.

From X we shall construct several geometric, algebraic, and combinatorial objects such as the cone they generate, a hyperplane arrangement, some families of convex polytopes, certain algebras and modules, and some special functions. Our aim is to show how these constructions relate to each other, and taken together, they provide structural understanding and computational techniques.

Keywords

Extremal Point Regular Point Pointed Cone Convex Polyhedron Relative Interior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “La Sapienza”RomaItaly

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