English

Hypergraph Characterization of Fusion Rings

Combinatorics 2026-03-10 v2

Abstract

We present a correspondence between multiplicity-free, self-dual, fusion rings and a digraph, hypergraph pair (D,H)(D,H). This correspondence is used to provide a complete characterization of all fusion rings corresponding to graphical properties of DD. 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.

Cite

@article{arxiv.2505.00180,
  title  = {Hypergraph Characterization of Fusion Rings},
  author = {Paul Bruillard and Kathleen Nowak and Stephen J. Young},
  journal= {arXiv preprint arXiv:2505.00180},
  year   = {2026}
}
R2 v1 2026-06-28T23:17:27.538Z