Hypergraph Characterization of Fusion Rings

Published 30 Apr 2025 in math.CO | (2505.00180v1)

Abstract: We present a correspondence between multiplicity-free, self-dual, fusion rings and a digraph, hypergraph pair $(D,H)$. This correspondence is used to provide a complete characterization of all fusion rings corresponding to graphical properties of $D$. Further, we exploit this correspondence to provide a complete list of all non-isomorphic, self-dual, multiplicity-free fusion rings of rank at most 8.

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