{"product_id":"theory-of-association-schemes-9783642065569","title":"Theory of Association Schemes","description":"\u003cp\u003e • Author(s): Paul-Hermann Zieschang\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Group Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45282402599063,"sku":"9783642065569","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783642065569.webp?v=1769302046","url":"https:\/\/atlanticbooks.com\/products\/theory-of-association-schemes-9783642065569","provider":"Atlantic Books","version":"1.0","type":"link"}