Association schemes

An association scheme is a way to organize and study relationships within a set of objects by dividing their pairings into categories based on how they relate. Think of it as creating a detailed map of connections, where each category groups pairs with similar interaction patterns. This structure helps mathematicians analyze symmetry and patterns within complex systems, like social networks or molecules. Essentially, association schemes provide a framework to understand the structure of connections in a systematic and symmetric way, revealing underlying patterns and properties.