Akopyan, A;
Bárány, I;
Robins, S;
(2017)
Algebraic vertices of non-convex polyhedra.
Advances in Mathematics
, 308
pp. 627-644.
10.1016/j.aim.2016.12.026.
Preview |
Text
Barany_1508.07594.pdf - Accepted Version Download (211kB) | Preview |
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.
| Type: | Article |
|---|---|
| Title: | Algebraic vertices of non-convex polyhedra |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.aim.2016.12.026 |
| Publisher version: | http://dx.doi.org/10.1016/j.aim.2016.12.026 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Polytope algebraVerticesTangent conesFourier–Laplace transform |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1536774 |
Archive Staff Only
 |
View Item |
