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Popular distances in 3-space |
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| Authors: | Paul Erd s Gergely Harcos and J nos Pach |
| Institution: | a Mathematical Institute of the Hungarian Academy of Sciences, H-1364, Budapest, P.O. Box, 127, Hungary b Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA c Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA |
| Abstract: | Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn1/3 log log n  m(n) n3/5 β(n), where c> 0 is a constant and β(n) is an extremely slowly growing function, related to the inverse of the Ackermann function. |
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