A problem of Kusner on equilateral sets
| dc.creator | Swanepoel, Konrad J. | |
| dc.date | 2003-09-19 | |
| dc.date | 2006-09-07 | |
| dc.date.accessioned | 2026-07-07T06:35:43Z | |
| dc.date.available | 2026-07-07T06:35:43Z | |
| dc.description | R. B. Kusner [R. Guy, Amer. Math. Monthly 90 (1983), 196--199] asked whether a set of vectors in a d-dimensional real vector space such that the l-p distance between any pair is 1, has cardinality at most d+1. We show that this is true for p=4 and any d >= 1, and false for all 1<p<2 with d sufficiently large, depending on p. More generally we show that the maximum cardinality is at most $(2\lceil p/4\rceil-1)d+1$ if p is an even integer, and at least $(1+ε_p)d$ if 1<p<2, where $ε_p>0$ depends on p. | |
| dc.description | 6 pages. Small correction to Proposition 2 | |
| dc.identifier | https://arxiv.org/abs/math/0309317 | |
| dc.identifier | http://arxiv.org/abs/math/0309317 | |
| dc.identifier | Archiv der Mathematik (Basel) 83 (2004), no. 2, 164--170 | |
| dc.identifier | doi:10.1007/s00013-003-4840-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99876 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 52C10 (Primary) 52A21, 46B20 (Secondary) | |
| dc.title | A problem of Kusner on equilateral sets | |
| dc.type | text |