Theory of Association Schemes
By: Zieschang, Paul-Hermann [author.].
Material type:
BookSeries: : Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: XVI, 284 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540305934.DDC classification: 512.2 | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| PK Kelkar Library, IIT Kanpur | Available | EBKS0006464 |
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. 0
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