Tight 9-designs on two concentric spheres

Details Tight 9-designs on two concentric spheres Tight 9-designs on two concentric spheres

2010-06-02

arxiv.org/abs/1006.0443v1

Mathematics

Combinatorics

14 pages

Scientific paper

The main purpose of this paper is to show the nonexistence of tight Euclidean
9-designs on 2 concentric spheres in $\mathbb R^n$ if $n\geq 3.$ This in turn
implies the nonexistence of minimum cubature formulas of degree 9 (in the sense
of Cools and Schmid) for any spherically symmetric integrals in $\mathbb R^n$
if $n\geq 3.$

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