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This article is cited in 3 scientific papers (total in 3 papers)
A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes
Eiichi Bannaia, Etsuko Bannaib, Yan Zhua a Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240 China
b Misakigaoka 2-8-21, Itoshima-shi, Fukuoka, 819-1136, Japan
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.
Received in September 2014
Citation:
Eiichi Bannai, Etsuko Bannai, Yan Zhu, “A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 209–223; Proc. Steklov Inst. Math., 288 (2015), 189–202
Linking options:
https://www.mathnet.ru/eng/tm3611https://doi.org/10.1134/S0371968515010148 https://www.mathnet.ru/eng/tm/v288/p209
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