Spherical two-distance sets
| dc.creator | Musin, Oleg R. | |
| dc.date | 2008-01-24 | |
| dc.date | 2008-07-02 | |
| dc.date.accessioned | 2026-07-07T12:58:45Z | |
| dc.date.available | 2026-07-07T12:58:45Z | |
| dc.description | A set S of unit vectors in n-dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b, and inner products of distinct vectors of S are either a or b. The largest cardinality g(n) of spherical two-distance sets is not exceed n(n+3)/2. This upper bound is known to be tight for n=2,6,22. The set of mid-points of the edges of a regular simplex gives the lower bound L(n)=n(n+1)/2 for g(n. In this paper using the so-called polynomial method it is proved that for nonnegative a+b the largest cardinality of S is not greater than L(n). For the case a+b<0 we propose upper bounds on |S| which are based on Delsarte's method. Using this we show that g(n)=L(n) for 6<n<22, 23<n<40, and g(23)=276 or 277. | |
| dc.description | 9 pages, (v2) several small changes and corrections suggested by referees, accepted in Journal of Combinatorial Theory, Series A | |
| dc.identifier | https://arxiv.org/abs/0801.3706 | |
| dc.identifier | http://arxiv.org/abs/0801.3706 | |
| dc.identifier | Journal of Combinatorial Theory, Series A 116 (2009) 988--995 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225347 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Spherical two-distance sets | |
| dc.type | text |