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.
  • ISBN13: 9783540261360
  • Publisher: Springer
  • Pubilcation Year: 2005
  • Format: Hardcover
  • Pages: 00284
SeriesSpringer Monographs in Mathematics
Publication DateOctober 20, 2005

Theory of Association Schemes

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