Theory of Association Schemes

Zusatztext

The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or a scheme as we shall say brie?y), and in order to do so we ?x a set and call it X. We write 1 to denote the set of all pairs (x,x) with x? X. For each subset X ? r of the cartesian product X×X, we de?ne r to be the set of all pairs (y,z) with (z,y)? r.For x an element of X and r a subset of X× X, we shall denote by xr the set of all elements y in X with (x,y)? r. Let us ?x a partition S of X×X with?? / S and 1 ? S, and let us assume X ? that s ? S for each element s in S. The set S is called a scheme on X if, for any three elements p, q,and r in S, there exists a cardinal number a such pqr ? that|yp?zq| = a for any two elements y in X and z in yr. pqr The notion of a scheme generalizes naturally the notion of a group, and we shall base all our considerations on this observation. Let us, therefore, brie?y look at the relationship between groups and schemes.

Autorenportrait

<P>Paul-Hermann Zieschang received a Doctor of Natural Sciences and the Habilitation in Mathematics from the Christian-Albrechts-Universität zu Kiel. He is also Extraordinary Professor of the Christian-Albrechts-Universität zu Kiel. Presently, he holds the position of an Associate Professor at the University of Texas at Brownsville. He held visiting positions at Kansas State University and at Kyushu University in Fukuoka.</P>

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