Geometric permutations of non-overlapping unit balls revisitedReport as inadecuate




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1 KAIST - Department of Electrical Engineering Korea Advanced Institute of Science and Technology 2 LIGM - Laboratoire d-Informatique Gaspard-Monge 3 Aarhus University Aarhus

Abstract : Given four congruent balls A, B, C, D in Rδ 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 counterexample of a highly degenerate nature in the algebraic sense.

Keywords : Transversal theory Line transversal Unit ball Congruent balls Geometric permutation





Author: Jae-Soon Ha - Otfried Cheong - Xavier Goaoc - Jungwoo Yang -

Source: https://hal.archives-ouvertes.fr/



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