Hypergraph Characterization of Fusion Rings

2025/04/30 by Bruillard, Paul, Nowak, Kathleen, Young, Stephen J.
#05E16 #05E40 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.00180

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.

Citations

• On Low-Rank Multiplicity-Free Fusion Categories
• On Low Rank Fusion Rings
• Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six
• Pseudo-unitary non-self-dual fusion categories of rank 4
• Practical graph isomorphism, II
• On braided fusion categories I
• On braided fusion categories I
• A finiteness property for braided fusion categories
• Graph Minors and Minimum Degree
• Weakly group-theoretical and solvable fusion categories
• Pre-modular categories of rank 3
• Fusion categories of rank 2
• On fusion categories
• Module categories, weak Hopf algebras and modular invariants
• Topological Quantum Computation

Related

• On Low Rank Fusion Rings
• On Low-Rank Multiplicity-Free Fusion Categories
• Fixed-point-free fusion automorphisms
• Fusion Rings over Drinfeld Doubles
• Rank 2 fusion rings are complete intersections