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A survey on tight Euclidean t-designs and tight relative t-designs in certain association schemes

  • Eiichi Bannai
  • Etsuko Bannai
  • Yan Zhu
Article

Abstract

It is known that there is a close analogy between the two relations “Euclidean t-designs vs. spherical t-designs” and “relative t-designs in binary Hamming association schemes vs. combinatorial t-designs.” We first look at this analogy and survey the known results, putting emphasis on the study of tight relative t-designs in certain Q-polynomial association schemes. We then specifically study tight relative 2-designs on two shells in binary Hamming association schemes H(n, 2) and Johnson association schemes J(v, k). The purpose of this paper is to convince the reader that there is a rich theory even for these special cases and that the time is ripe to study tight relative t-designs more systematically for general Q-polynomial association schemes.

Keywords

Weight Function Orthonormal Basis STEKLOV Institute Association Scheme Cubature Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.FukuokaJapan

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