Greedy fusion
arXiv:2607.13126
summary
The paper shows that integer sequences of formal codegrees, inspired by the greedy algorithm for unit‑fraction decompositions of 1, constrain the possible structures of fusion rings, and proves that a fusion ring with formal codegrees 2, 3, and 7 cannot be categorified.
Abstract
We demonstrate that certain sequences of integer formal codegrees, motivated by the greedy algorithm for unit fraction decompositions of 1, dictate the structure of fusion rings. In particular, no fusion ring that has formal codegrees 2, 3, and 7 is categorifiable.
8 pages
Topics & keywords
#fusion rings#formal codegrees#categorification#greedy algorithm#unit fraction decompositionformal codegreesfusion ringcategorifiablegreedy algorithminteger sequencesunit fractions