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this case. Our result settles a conjecture in combinatorial geometry.” Reviewed by Luiz Henrique de Figueiredo References

By Yingping (-ndm-cs) Xu, Jinhui (-sunyb-cse) Chen, Danny Z. (-ndm-cs, P. K. Agarwal, B. Aronov and M. Sharir


Geometric permutations of higher dimensional spheres. (English summary) Comput. Geom. 29 (2004), no. 1, 47–60. Summary: “In this paper, we prove that the maximum number of geometric permutations (induced by line transversals) of a set of n pairwise disjoint spheres with a bounded radius ratio in R d for d ≥ 3 is at most 2 ⌊ √ 2M⌋+1, where M is the ratio of the largest radius and the smallest radius of the spheres. Setting M to 1, this gives an upper bound of 4 on the maximum number of geometric permutations for congruent spheres in R d, matching a recently independently discovered resul

Year: 2013
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