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Springer Monographs in Mathematics

Theory of Association Schemes

Authors: Zieschang, Paul-Hermann

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About this book

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.

About the authors

Paul-Hermann Zieschang received a Doctor of Natural Sciences and the Habilitation in Mathematics from the Christian-Albrechts-Universität zu Kiel. He is also Extraordinary Professor of the Christian-Albrechts-Universität zu Kiel. Presently, he holds the position of an Associate Professor at the University of Texas at Brownsville. He held visiting positions at Kansas State University and at Kyushu University in Fukuoka.

Reviews

From the reviews:

"Theory of association schemes is a self-contained textbook. … The theory of association schemes can be applied to Hecke algebras of transitive permutation groups, and the algebras are usually noncommutative. So this treatment is also good for group theorists. … The book under review also contains many recent developments in the theory." (Akihide Hanaki, Mathematical Reviews, 2006 h)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-540-30593-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-540-26136-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-06556-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Association Schemes
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-30593-4
DOI
10.1007/3-540-30593-9
Hardcover ISBN
978-3-540-26136-0
Softcover ISBN
978-3-642-06556-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVI, 284
Topics

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