On higher indicators of regular association schemes
On higher indicators of regular association schemes
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论定期联谊计划的更高指标
DOI：
10.1016/j.disc.2018.04.006
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发表时间：
2018
影响因子：
0.8
通讯作者：
Yoshikawa Masayoshi
中科院分区：
文献类型：
--
作者：
山本 康太;Shigeki Akiyama;Takuya Ikuta;Yoshikawa Masayoshi
本文定义了结合概型的高阶Frobenius-Schur指标和高阶Frobenius-Schur指标，作为有限群的高阶Frobenius-Schur指标和高阶Frobenius-Schur指标的推广。任何关联方案的较高指标总是正有理数。特别地，对于任何正整数n，任何正则结合方案的第n个指示符是使得其强围长整除n的关系的数目。因此，任何规则关联方案的所有较高指示符都是自然数，并且指示符的序列是周期性的。我们将证明这些事实的逆对于有限指数结合方案也成立。最后，我们引入了一族高阶指标为自然数且指标序列为周期的无穷指数结合方案。
In the present paper, we will define the higher Frobenius–Schur indicators and the higher indicators of association schemes as a generalization of those of finite groups. The higher indicators of any association scheme are always positive rational numbers. Especially, for any positive integer n, the n th indicator of any regular association scheme is the number of relations such that its strong girth divides n. Thus, all higher indicators of any regular association scheme are natural numbers, and the sequence of the indicators is periodic. We will show that the converses of these facts are also true for finite exponent association schemes. Finally, we introduce a family of infinite exponent association schemes all higher indicators of which are natural numbers and the sequence of the indicators of which is periodic.