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＜電子ブック＞
Theory of Association Schemes / by Paul-Hermann Zieschang
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	XVI, 284 p : online resource
著者標目	*Zieschang, Paul-Hermann author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Discrete mathematics LCSH:Geometry FREE:Group Theory and Generalizations FREE:Discrete Mathematics FREE:Geometry
一般注記	Basic Facts -- Closed Subsets -- Generating Subsets -- Quotient Schemes -- Morphisms -- Faithful Maps -- Products -- From Thin Schemes to Modules -- Scheme Rings -- Dihedral Closed Subsets -- Coxeter Sets -- Spherical Coxeter Sets 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 HTTP:URL=https://doi.org/10.1007/3-540-30593-9

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