On neighbors in geometric permutations Conference Paper uri icon

abstract

  • 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.

publication date

  • January 1, 2002