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 ...
Read More
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.
Read Less
Add this copy of Theory of Association Schemes (Springer Monographs in to cart. $64.56, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2005 by Springer.
Add this copy of Theory of Association Schemes to cart. $112.32, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2010, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Theory of Association Schemes to cart. $112.32, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2005 by Springer.
Add this copy of Theory of Association Schemes to cart. $122.45, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2005 by Springer.
