Theory of Association Schemes (Springer Monographs in Mathematics)

Zieschang, Paul-Hermann

Springer（2005発売）

Springer（2005発売）

• 製本 Hardcover:ハードカバー版／ページ数 300 p.
• 商品コード 9783540261360

Full Description

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 XxX, 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 Xx 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 XxX 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.

Contents

Basic Facts.- Closed Subsets.- Generating Subsets.- Quotient Schemes.- Morphisms.- Faithful Maps.- Products.- From Thin Schemes to Modules.- Scheme Rings.- Dihedral Closed Subsets.- Coxeter Sets.- Spherical Coxeter Sets.