Association Schemes: Designed Experiments, Algebra and Combinatorics

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Cambridge University Press, Feb 26, 2004 - Mathematics
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Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.
 

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Contents

Association schemes
1
The BoseMesner algebra
31
Combining association schemes
59
Incompleteblock designs
79
Partial balance
111
Families of partitions
145
Designs for structured sets
171
Exercises
222
Exercises
275
Subschemes quotients duals and products
277
Association schemes on the same set
301
Where next?
329
History and references
343
Glossary of notation
355
References
367
Index
381

Exercises
252

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