Association Schemes: Designed Experiments, Algebra and Combinatorics
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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Abelian group adjacency matrices ancestral subsets associate classes association scheme association scheme defined ation scheme automorphism balanced design balanced incomplete-block design balanced with respect block design blueprint Bose-Mesner algebra canonical efficiency factors character table commutative contains Corollary cube cyclic design Definition design in Example design is partially diagonal dimensions distance-regular graph edge eigenspaces eigenvalues elements entries equal Equation estimator F-class gonal group-divisible association scheme Hasse diagram Hence inherent partition integers inverse isomorphism Latin square lattice designs Lemma Let Q linear combination minimal polynomial mutually orthogonal n-set orthogonal block structure orthogonal projector pair partial order partially balanced partition F Petersen graph poset block structure pre-orders Proof Qi and Q2 Qi x Q2 rectangles revisited row-column design scheme Q second associates shows strata stratum projectors strongly regular graph subspace symmetric Technique Theorem valencies variance vector vertices wreath product