{"product_id":"theory-of-association-schemes-paul-hermann-zieschang-9783540261360","title":"Theory of Association Schemes","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Paul-Hermann Zieschang\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3540261362\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783540261360\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/20\/2005\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 284\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.17lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 6.44h x 9.45w x 0.64d","brand":"Paul-Hermann Zieschang","offers":[{"title":"Hardcover","offer_id":47579926036735,"sku":"9783540261360","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_63d557e1-8d1a-49e5-b569-cfa3c8ae77db.jpg?v=1763877617","url":"https:\/\/www.whiterainbookhouse.com\/products\/theory-of-association-schemes-paul-hermann-zieschang-9783540261360","provider":"WR Book House","version":"1.0","type":"link"}