Year: 2026
Type: preprint
Abstract: We study representations for relation algebras corresponding to certain edge colourings of complete graphs. Previously suitable colourings were obtained for the number of colours $n$ up to $2000$, with two exceptions: $n = 8$ and $n = 13$. Using a method that we have called the FBF (Fusion Beautiful Fusions) method, we find colourings for $8$ and $13$ colours. Our method is a new guess-and-check approach that we describe as an adaptation of Comer's finite-field method. Using FBF we construct novel colourings that are non-isomorphic to existing published colourings for 5, 6, 7, 9, 10, 11 and 12 colours.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214228425