Coherent configurations

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as the group case, the admissable relations are the invariant binary relations in the sense of Wielandt [20] and the adjacency ring is the centralizer ring of the permutation representation. Thus coherent configurations provide a combinatorial setting for centralizer ring theory of permutation representations on the one hand, and the possibility of applying methods of centralizer ring theory to combinatorics on the other. In practice, such processes as fusion (see Section 10) may produce coherent configurations