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$\DeclareMathOperator\ch{ch}$$\DeclareMathOperator\FPdim{FPdim}$We refer to [EGNO15, Chapter 3] for the notion of fusion ring and basic results. The type of a fusion ring $R$ is the list $(\FPdim(b_i)...

In this answer, Geoff ruled out the existence of a finite group $G$ such that the fusion category $\mathrm{Rep}(G)$ has simple objects $5_1$ and $7_1$ of FPdim $5$ and $7$ resp., with (for some object ...

A cyclic number is a natural number $n$ such that any group of order $n$ is cyclic. A003277 Theorem (T. Szele, 1947): A number $n$ is cyclic if and only if it is coprime to its Euler totient $\varphi(...

Warning: this post is the "numerical" analog of Are there workable algebraic geometry approaches for the pentagon equation? I've replaced "algebraic geometry" by "numerical" in its content, ...

A pentagon equation is a system of polynomial equations of degree $3$ with several variables and integer coefficients, given by a fusion ring. A fusion ring is given by a finite set of integer ...