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 ? thatyp?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.
| Author: Paul-Hermann Zieschang |
| Publisher: Springer |
| Publication Date: Oct 20, 2005 |
| Number of Pages: 284 pages |
| Binding: Hardback or Cased Book |
| ISBN-10: 3540261362 |
| ISBN-13: 9783540261360 |
