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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 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.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 284
- Langue:
- Anglais
- Collection :
Caractéristiques
- EAN:
- 9783642065569
- Date de parution :
- 21-10-10
- Format:
- Livre broché
- Format numérique:
- Trade paperback (VS)
- Dimensions :
- 156 mm x 234 mm
- Poids :
- 421 g
