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- W2991490850 abstract "A relation s of an association scheme is called regular if s∗ss={s}. In Yoshikawa (2015), it was shown that, for each regular relation s of an association scheme S, s∗s is a closed subset of S. In the present article, we show that, for each regular relation s of an association scheme S, 〈s〉∕∕s∗s is a cyclic group the order of which coincides with the strong girth of s. As an immediate application of this result we obtain that the strong girth of a regular relation of an association scheme S divides the order of S. As an application to the theory of characters of association schemes we obtain a generalization of Burnside’s vanishing theorem to regular association schemes, that is to association schemes all relations of which are regular. Our theorem says that each irreducible complex character of a regular association scheme S with multiplicity greater than 1 vanishes on at least one relation of S." @default.
- W2991490850 created "2019-12-05" @default.
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- W2991490850 date "2020-03-01" @default.
- W2991490850 modified "2023-09-25" @default.
- W2991490850 title "On closed subsets generated by a regular relation of an association scheme" @default.
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- W2991490850 doi "https://doi.org/10.1016/j.disc.2019.111706" @default.
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