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On the rigidity of sphericalt-designs that are orbits of finite reflection groups

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Abstract

The concept of rigid sphericalt-designs was introduced by Bannai. He conjectured that there is a functionf(t, d) such that ifX is a sphericalt design in thed-dimensional Euclidean space so that |X|>f(t, d), theX is non-rigid. Furthermore, he asked to find examples of rigid but not tight sperical designs. In the present article we shall investigate the case whenX is an orbit of a finite reflection group and prove thatX is rigid iff tight for the groupsA n ,B n ,C n ,D n ,E 6,E 7,F 4,I 3.

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Author notes

  1. Attila Sali

    Present address: Math Inst. of Hung. Acad. Sci., P.o.b. 127, H-1364, Budapest, Hungary

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyushu University, Higashi-ku, Hakozaki 6-10-1, Postal No. 812, Fukuoka, Japan

    Attila Sali

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  1. Attila Sali
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Additional information

Communicated by E. Bannai

Research was partially supported by Hungarian National Research fund Grant No. 4267.

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Sali, A. On the rigidity of sphericalt-designs that are orbits of finite reflection groups. Des Codes Crypt 4, 157–170 (1994). https://doi.org/10.1007/BF01578869

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  • DOI: https://doi.org/10.1007/BF01578869

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