报告题目：On tight relative $t$-designs

报告人：Eiichi Bannai 
       (上海交通大学)

报告时间：2013年10月25日下午 2:45-3:45

报告地点：管理楼1518教室

报告摘要：Euclidean $t$-designs are a two-step generalization of spherical $t$-designs. Relative $t$-designs in binary Hamming association scheme $H(n,2)$ is a two-step generalization of combinatorial $t$-designs. We will discuss how much we can imitate the theory of Euclidean $t$-designs, in the study of relative $t$-designs  in $H(n,2)$, in particular of tight relative $t$-designs in $H(n,2).$ We obtain the following explicit results on tight relative $t$-designs in $H(n,2)$.

(i) For a tight relative $2e$-design in $H(n,2)$, the weight function must be constant on each shell.

(ii) For a tight relative $2$-design on two shells in $H(n, 2)$, the structure of coherent configuration is attached.

(iii) We can classify tight relative $2$-designs on two shells in $H(n, 2)$ for small $n$, say $n￥leq  30$.

(iv) We discovered a family of tight relative $2$-designs on two shells in $H(n, 2)$, which are the first such example with a non constant weight function.

We will also study similar results for more general association schemes. The contents of this talk are based on the following two joint papers with other authors.

(1) Eiichi Bannai, Etsuko Bannai, Sho Suda and Hajime Tanaka: On relative t-designs in polynomial association schemes, arXiv:1303.7163.

(2) Eiichi Bannai, Etsuko Bannai and Hideo Bannai: On the existence of tight relative $2$-designs on binary Hamming association schemes, arXiv:1304.5760.

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