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Compact symmetric triads and symmetric triads with multiplicities
Kurando Baba, Osamu Ikawa
https://arxiv.org/abs/2506.02511 https://…

Compact symmetric triads and symmetric triads with multiplicities
In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative compact symmetric triads. As applications, we give the classifications for commutative compact symmetric triads, which consist of two types depending on the choice of the equivalence relations.