Algebraic vertices of non-convex polyhedra

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• 作者：Arseniy Akopyan^a ; ^{akopjan@gmail.com} ; Imre Bá ; rá ; ny^b ; ^c ; ^{barany@renyi.hu} ; Sinai Robins^d ; ^{sinai.robins@gmail.com}
• 关键词：primary ; 52B11 ; 51M20 ; secondary ; 44A10
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：627-644
• 全文大小：397 K
• 卷排序：308

文摘

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.