2024/03/31 by Edwin van Dam, van Dam, Edwin R., Jack H. Koolen +3
Engineering · Materials Science · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #Material Dynamics and Properties #Metallic Glasses and Amorphous Alloys #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2404.00567
openalex publication_date 2024/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a fusion scheme. We define the fusing-relations graph on the set of relations, where a pair forms an edge if it fuses. We show that if the fusing-relations graph is connected but not a path, then the association scheme is amorphic. As a side result, we show that if an association scheme has at most one relation that is neither strongly regular of Latin square type nor strongly regular of negative Latin square type, then it is amorphic.