Fractional Helly theorem for the diameter of convex sets
نویسنده
چکیده
We provide a new quantitative version of Helly’s theorem: there exists an absolute constant α > 1 with the following property: if {Pi : i ∈ I} is a finite family of convex bodies in R with int (⋂ i∈I Pi ) 6= ∅, then there exist z ∈ R, s 6 αn and i1, . . . is ∈ I such that z + Pi1 ∩ · · · ∩ Pis ⊆ cn 3/2 ( z + ⋂
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