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Theory of Association Schemes / Edition 1
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Theory of Association Schemes / Edition 1
Current price: $109.99
Barnes and Noble
Theory of Association Schemes / Edition 1
Current price: $109.99
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The present text is an introduction to the theory of association schemes. We start with the definition of an association scheme (or a scheme as we shall say briefly), and in order to do so wex 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 define 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 usx 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, briefly look at the relationship between groups and schemes.