Theory of Association Schemes

"Theory of Association Schemes" is the first concept-oriented treatment of the structure theory of association schemes. It contains several recent results which appear for the first time in text book form. The generalization of Sylow's group-theoretical theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits' main theorem on buildings of spherical type. Also a scheme-theoretical characterization of Glauberman's Z-involutions is included. The text is self-contained and accessible for advanced undergraduate students.