2014/07/03 by Jae-Soon Ha, Otfried Cheong, Ha, Jae-Soon +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG
paper · pdf · doi:10.48550/arxiv.1407.0795
arxiv created 2014/07/03 · openalex publication_date 2014/07/03 · arxiv updated 2014/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given four congruent balls A, B, C, D in Rd that have disjoint interior and admit a line that intersects them in the order ABCD, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of A and D. This allows us to give a new short proof that n interior-disjoint congruent balls admit at most three geometric permutations, two if n≥ 7. We also make a conjecture that would imply that n≥ 4 such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature.