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Djoko Suprianto
Combinatorial Mathematics Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung 40132, INDONESIA.
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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On Tight Euclidean 6-Designs: An Experimental Result Djoko Suprianto
Journal of Mathematical and Fundamental Sciences Vol. 43 No. 1 (2011)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.sci.2011.43.1.3

Abstract

A finite set n X ⊆ ℝn with a weight function w: X → â„ > 0 is called Euclidean t-design in â„ > 0 (supported by p concentric spheres) if the following condition holds:           1 i p i  i i S x X w X f d w f S      x x  x x for any polynomial f(x) ∈ Polℝ > 0 of degree at most t. Here Si ℝn is a sphere of radius ri ≥ 0, Xi=X ∩ S, and σi(x) is an O(n) -invariant measure on Si such that |Si|=rin-1|Sn-1>|, with |Si| is the surface area of Si and |Sn-1|is a surface area of the unit sphere in ℝn. Recently, Bajnok [1] constructed tight Euclidean t-designs in the plane (n=2) for arbitrary t and p . In this paper we show that for case t=6 and p=2 , tight Euclidean 6-designs constructed by Bajnok is the unique configuration in â„œn, for 2 ≤ n ≤ 8.
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