Akopyan, A. and Bárány, Imre and Robins, S. (2017) Algebraic vertices of nonconvex polyhedra. ADVANCES IN MATHEMATICS, 308. pp. 627644. ISSN 00018708

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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 linecones. 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 nonzero Fourier–Laplace transform. © 2016 Elsevier Inc.
Item Type:  Article 

Uncontrolled Keywords:  VERTICES; Tangent cones; Polytope algebra; Fourier–Laplace transform 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  12 Jul 2017 09:07 
Last Modified:  12 Jul 2017 09:07 
URI:  http://real.mtak.hu/id/eprint/55890 
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