Krein conditions for coherent configurations Original Research Article

A coherent configuration can be thought of as a set of association schemes linked by additional relations. We develop a generalization of the Krein conditions which applies to coherent configurations and which takes into account the additional information contained in the relations between the schemes. We then apply it to quasisymmetric designs and strongly regular designs to obtain inequalities on the parameters. We also give examples to show that these conditions are stronger than the usual Krein conditions on the association schemes contained in the configuration.