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 XX, 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 XX with / S and 1 ? S, and let us assume X ? that s ? S for each element...
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 shal...
This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition),...
This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are...
