Algebraic vertices of non-convex polyhedra
Akopyan, Arseniy
Bárány, Imre
Robins, Sinai
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.
Academic Press
2017
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/1180
Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. <i>Advances in Mathematics</i>. 2017;308:627-644. doi:<a href="https://doi.org/10.1016/j.aim.2016.12.026">10.1016/j.aim.2016.12.026</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2016.12.026
info:eu-repo/semantics/altIdentifier/issn/00018708
info:eu-repo/grantAgreement/EC/FP7/291734
info:eu-repo/semantics/openAccess