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02782nam a22004815i 4500 |
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978-3-540-30593-4 |
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|a 9783540305934
|9 978-3-540-30593-4
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|a 10.1007/3-540-30593-9
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|a QA174-183
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|a MAT002010
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|a 512.2
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|a Zieschang, Paul-Hermann.
|e author.
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|a Theory of Association Schemes
|h [electronic resource] /
|c by Paul-Hermann Zieschang.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2005.
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|a XVI, 284 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Springer Monographs in Mathematics,
|x 1439-7382
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|a 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.
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|a 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.
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|a Mathematics.
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|a Group theory.
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|a Geometry.
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|a Combinatorics.
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|a Mathematics.
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|a Group Theory and Generalizations.
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|a Combinatorics.
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|a Geometry.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783540261360
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|a Springer Monographs in Mathematics,
|x 1439-7382
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|u http://dx.doi.org/10.1007/3-540-30593-9
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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