Geometric permutations of disjoint translates of convex sets
Discrete Mathematics
The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2
Discrete & Computational Geometry
Discrete & Computational Geometry
The different ways of stabbing disjoint convex sets
Discrete & Computational Geometry
Helly-type theorems and geometric transversals
Handbook of discrete and computational geometry
Geometric permutations of high dimensional spheres
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The triples of geometric permutations for families of disjoint translates
Discrete Mathematics
Forbidden Families of Geometric Permutations in ℝd
Discrete & Computational Geometry
Hadwiger and Helly-type theorems for disjoint unit spheres in R3
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On geometric permutations induced by lines transversal through a fixed point
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Line transversals to disjoint balls
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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We show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric permutations if n ≥ 9, and at most three if 3 ≤ n ≤ 8. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in R3: if any subset of size at most 18 of a family of such spheres admits a line transversal, then there is a line transversal for the entire family.