$Q$-polynomial coherent configurations

Abstract

Coherent configurations are a generalization of association schemes. In this paper, we introduce the concept of Q-polynomial coherent configurations and study the relationship among intersection numbers, Krein numbers, and eigenmatrices. The examples of Qpolynomial coherent configurations are provided from Delsarte designs in Q-polynomial schemes and spherical designs.

Distance-regular graphs, the subconstituent algebra, and the $Q$-polynomial property

“…Remark 20.9. In [58] Sho Suda introduced the Q-polynomial property for coherent configurations. A coherent configuration is a combinatorial object more general than a graph.…”

“…Then (58) holds. In (58), multiply each term on the left by E i and on the right by E j . Simplify the result to get…”