Association Schemes

Erscheinungsjahr 2015
ISBN: 978-0-521-82446-0
Verlag: Cambridge University Press

Buch, Englisch, Band 84, 406 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 807 g

Reihe: Cambridge Studies in Advanced Mathematics

Association schemes are of interest to both mathematicians and statisticians and this book is 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 some recent research. This book has arisen 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 bring their understanding of association schemes up to the current state of the art.

Autoren/Hrsg.

Bailey, R. A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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.

Über Autor(innen)

Bailey, R. A.
R. A. Bailey has been Professor of Statistics at Queen Mary, University of London since 1994. Currently she is also head of the School of Mathematical Sciences. After doing a DPhil in group theory at Oxford she worked in the Mathematics Faculty of the Open University then took a post-doctoral research fellowship in Statistics at Edinburgh University. Since then her main research interest has been in the design of experiments. She spent 10 years in the Statistics Department of Rothamsted Experimental Station (now the BBSRC Institute of Arable Crops Research) before coming to the University of London as Professor of Mathematical Sciences at Goldsmiths' College. Along the way she was a school teacher for one year and a technician in medical research for another. She has also held short-term appointments at the Universities of Western Australia, Sydney (Australia), and North Carolina at Chapel Hill (USA). She has been a frequent visitor to the Unit\'e de Biom\'etrie in the Institut National de la Recherche Agronomique at Versailles (France), and has given short courses on Statistics in Finland, Buenos Aires (Argentina) and Augsburg (Germany). Her interests span statistics and pure mathematics, and the importance of both to scientists and to ordinary people. She has served the London Mathematical Society as Meetings and Membership Secretary, Vice President and member of the Personnel and Office Committee. She was a member of the British Combinatorial Committee when it established its current successful format for conferences. She was secretary of the UK \TeX\ Users' Group for four years. She is a member of the Council of the International Biometric Society, being president of the British Region 2000-2002. She is a member of the Research Section of the Royal Statistical Society. She is also a member of the Institute of Mathematical Statistics and the International Statistical Institute. She represented the Committee of Professors of Statistics first on the Higher Educatio