Association scheme

Summary

An association scheme is a partition of the ordered pairs of a finite set into relations with a strong regularity property. The number of paths of two given types between two points depends only on the relation between the points. The adjacency matrices of the relations span a matrix algebra, the Bose–Mesner algebra, which makes linear algebra available for combinatorial questions. Association schemes came from the design of statistical experiments and are now basic in coding theory, design theory and the study of strongly regular graphs.