Association Schemes Designed Experiments, Algebra and Combinatorics [Paperback]

This book covers association schemes for graduate mathematicians and statisticians, minimum prerequisites, numerous examples and exercises.This book has arisen from a graduate course taught by R.A. Bailey at the University of London. She discusses the mathematics of association schemes, an area lying between pure maths and statistics that relates to the optimal design of scientific experiments. Care has been taken to make the book accessible to both pure mathematicians and statisticians alike. The level is that of a graduate student, but this book will appeal to researchers as an accessible reference work from which to learn about the statistical/combinatorial aspect of their work.This book has arisen from a graduate course taught by R.A. Bailey at the University of London. She discusses the mathematics of association schemes, an area lying between pure maths and statistics that relates to the optimal design of scientific experiments. Care has been taken to make the book accessible to both pure mathematicians and statisticians alike. The level is that of a graduate student, but this book will appeal to researchers as an accessible reference work from which to learn about the statistical/combinatorial aspect of their work.R.A. Bailey covers in this study the mathematics of association schemes--an area lying between pure mathematics and statistics that relates to the optimal design of scientific experiments. The book is accessible to mathematicians as well as statisticians. Arising from a graduate course taught by the author, it appeals to students as well as researchers as a valuable reference work from which to learn about the statistical/combinatorial aspects of their work.1. Association schemes; 2. The BoseMesner 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 sal#§