The caratheodory number for thek-core

Abstract

Thek-core of the setS ⊂ℝn is the intersection of the convex hull of all setsA ⊆ S with ¦S∖A¦<-k. The Caratheodory number of thek-core is the smallest integerf (d,k) with the property thatx ∈ core kS, S ⊂ℝn implies the existence of a subsetT ⊆ S such thatx ∈ corekT and ¦T¦≤f (d, k). In this paper various properties off(d, k) are established.

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Research of this author was partially supported by Hungarian National Science Foundation grant no. 1812.

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Bárány, I., Perles, M. The caratheodory number for thek-core. Combinatorica 10, 185–194 (1990). https://doi.org/10.1007/BF02123009

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