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- W2215190454 abstract "Given four congruent balls A , B , C , D in R δ 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 that is algebraically highly degenerate." @default.
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- W2215190454 date "2016-02-01" @default.
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- W2215190454 title "Geometric permutations of non-overlapping unit balls revisited" @default.
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- W2215190454 doi "https://doi.org/10.1016/j.comgeo.2015.12.003" @default.
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