The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2
Discrete & Computational Geometry
Discrete & Computational Geometry
Visibility preprocessing for interactive walkthroughs
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Finding a line transversal of axial objects in three dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
The different ways of stabbing disjoint convex sets
Discrete & Computational Geometry
Shape sensitive geometric permutations
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SCG '01 Proceedings of the seventeenth 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
Set systems and families of permutations with small traces
European Journal of Combinatorics
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We introduce a new notion of 'neighbors' in geometric permutations. We conjecture that the maximum number of neighbors in a set S of n pairwise disjoint convex bodies in Rd is O(n), and we prove this conjecture for d = 2. We show that if the set of pairs of neighbors in a set S is of size N, then S admits at most O(Nd-1) geometric permutations. Hence, we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any finite family of pairwise disjoint convex bodies in the plane.