Algebraic vertices of non-convex polyhedra

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OA https://arxiv.org/abs/1508.07594 [Submitted Version]

Journal Article | Published | English

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Author
Akopyan, ArseniyISTA ; Bárány, Imre; Robins, Sinai
Department
Abstract
In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform.
Publishing Year
Date Published
2017-02-21
Journal Title
Advances in Mathematics
Publisher
Academic Press
Volume
308
Page
627 - 644
ISSN
IST-REx-ID
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