Inclusion–Exclusion Principles for Convex Hulls and the Euler Relation
نویسندگان
چکیده
منابع مشابه
Inclusion-Exclusion Principles for Convex Hulls and the Euler Relation
Abstract. Consider n points X1, . . . ,Xn in R and denote their convex hull by Π. We prove a number of inclusion-exclusion identities for the system of convex hulls ΠI := conv(Xi : i ∈ I), where I ranges over all subsets of {1, . . . , n}. For instance, denoting by ck(X) the number of k-element subcollections of (X1, . . . ,Xn) whose convex hull contains a point X ∈ R, we prove that c1(X) − c2(...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2017
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-017-9880-0