紹介
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. Originally published in 2004, 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.
目次
1. Association schemes
2. The Bose-Mesner algebra
3. Combining association schemes
4. Incomplete-block designs
5. Partial balance
6. Families of partitions
7. Designs for structured sets
8. Groups
9. Posets
10. Subschemes, quotients, duals and products
11. Association schemes on the same set
12. Where next?
13. History and references.
