Name
Abstract | ||
|---|---|---|
A Gaussian t-design is defined as a finite set X in the Euclidean space Rn satisfying the condition: 1V(Rn)∫Rnf(x)e−α2‖x‖2dx=∑x∈Xω(x)f(x) for any polynomial f(x) in n variables of degree at most t, where α is a constant real number and ω is a positive weight function on X. It is well known that if X is a Gaussian 2e-design in Rn, then |X|≥n+ee. We call X a tight Gaussian 2e-design in Rn if |X|=n+ee. In this paper, we prove that there exists no tight Gaussian 6-design supported by two concentric spheres in Rn for n≥2. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.disc.2013.01.023 | Discrete Mathematics |
Keywords | Field | DocType |
Gaussian t-designs,Spherical t-designs,Euclidean t-designs | Discrete mathematics,Combinatorics,Finite set,Concentric,Weight function,Polynomial,Euclidean space,Gaussian,SPHERES,Real number,Mathematics | Journal |
Volume | Issue | ISSN |
313 | 9 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bo Hou | 1 | 1 | 2.39 |
| Panpan Shen | 2 | 0 | 0.34 |
| Ran Zhang | 3 | 33 | 13.46 |
| Suogang Gao | 4 | 59 | 12.78 |