Name
Abstract | ||
|---|---|---|
Given four congruent balls A , B , C , D in R ¿ 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.comgeo.2015.12.003 | Computational Geometry: Theory and Applications |
Keywords | Field | DocType |
unit ball | Discrete mathematics,Degenerate energy levels,Combinatorics,Disjoint sets,Ball (bearing),Permutation,Congruence (geometry),Conjecture,Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
53 | C | 0925-7721 |
Citations | PageRank | References |
1 | 0.37 | 12 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jae-Soon Ha | 1 | 1 | 0.37 |
| Otfried Cheong | 2 | 594 | 60.27 |
| Xavier Goaoc | 3 | 138 | 20.76 |
| jungwoo yang | 4 | 1 | 0.37 |