Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- Acknowledgements -- 1 Association schemes -- 1.1 Partitions -- 1.2 Graphs -- 1.3 Matrices -- 1.4 Some special association schemes -- 1.4.1 Triangular association schemes -- 1.4.2 Johnson schemes -- 1.4.3 Hamming schemes -- 1.4.4 Distance-regular graphs -- 1.4.5 Cyclic association schemes -- Exercises -- 2 The Bose-Mesner algebra -- 2.1 Orthogonality -- 2.2 The algebra -- 2.3 The character table -- 2.4 Techniques -- 2.5 Parameters of strongly regular graphs -- Exercises -- 3 Combining association schemes -- 3.1 Tensor products -- 3.2 Crossing -- 3.3 Isomorphism -- 3.4 Nesting -- 3.5 Iterated crossing and nesting -- Exercises -- 4 Incomplete-block designs -- 4.1 Block designs -- 4.2 Random variables -- 4.3 Estimating treatment effects -- 4.4 Efficiency factors -- 4.5 Estimating variance -- 4.6 Building block designs -- 4.6.1 Juxtaposition -- 4.6.2 Inflation -- 4.6.3 Orthogonal superposition -- 4.6.4 Products -- Exercises -- 5 Partial balance -- 5.1 Partially balanced incomplete-block designs -- 5.2 Variance and efficiency -- 5.3 Concurrence and variance -- 5.4 Cyclic designs -- 5.5 Lattice designs -- 5.5.1 Simple lattice designs -- 5.5.2 Square lattice designs -- 5.5.3 Cubic and higher-dimensional lattices -- 5.5.4 Rectangular lattice designs -- 5.6 General constructions -- 5.6.1 Elementary designs -- 5.6.2 New designs from old -- 5.7 Optimality -- Exercises -- 6 Families of partitions -- 6.1 A partial order on partitions -- 6.2 Orthogonal partitions -- 6.3 Orthogonal block structures -- 6.4 Calculations -- 6.5 Orthogonal block structures from Latin squares -- 6.6 Crossing and nesting orthogonal block structures -- Exercises -- 7 Designs for structured sets -- 7.1 Designs on orthogonal block structures -- 7.1.1 Row-column designs -- 7.1.2 Nested blocks.

7.1.3 Nested row-column designs -- 7.1.4 Row-column designs with split plots -- 7.1.5 Other orthogonal block structures -- 7.2 Overall partial balance -- 7.3 Fixed effects -- 7.4 Random effects -- 7.5 Special classes of design -- 7.5.1 Orthogonal designs -- 7.5.2 Balanced designs -- 7.5.3 Cyclic designs -- 7.5.4 Lattice squares -- 7.6 Valid randomization -- 7.7 Designs on association schemes -- 7.7.1 General theory -- 7.7.2 Composite designs -- 7.7.3 Designs on triangular schemes -- 7.7.4 Designs on Latin-square schemes -- 7.7.5 Designs on pair schemes -- Exercises -- 8 Groups -- 8.1 Blueprints -- 8.2 Characters -- 8.3 Crossing and nesting blueprints -- 8.4 Abelian-group block-designs -- 8.5 Abelian-group designs on structured sets -- 8.6 Group block structures -- 8.7 Automorphism groups -- 8.8 Latin cubes -- Exercises -- 9 Posets -- 9.1 Product sets -- 9.2 A partial order on subscripts -- 9.3 Crossing and nesting -- 9.4 Parameters of poset block structures -- 9.5 Lattice laws -- 9.6 Poset operators -- Exercises -- 10 Subschemes, quotients, duals and products -- 10.1 Inherent partitions -- 10.2 Subschemes -- 10.3 Ideal partitions -- 10.4 Quotient schemes and homomorphisms -- 10.5 Dual schemes -- 10.6 New from old -- 10.6.1 Relaxed wreath products -- 10.6.2 Crested products -- 10.6.3 Hamming powers -- Exercises -- 11 Association schemes on the same set -- 11.1 The partial order on association schemes -- 11.2 Suprema -- 11.3 Inflma -- 11.4 Group schemes -- 11.5 Poset block structures -- 11.6 Orthogonal block structures -- 11.7 Crossing and nesting -- 11.8 Mutually orthogonal Latin squares -- Exercises -- 12 Where next? -- 12.1 Few parameters -- 12.2 Unequal replication -- 12.3 Generalizations of association schemes -- 13 History and references -- 13.1 Statistics -- 13.1.1 Basics of experimental design -- 13.1.2 Factorial designs.

13.1.3 Incomplete-block designs -- 13.1.4 Partial balance -- 13.1.5 Orthogonal block structures -- 13.1.6 Multi-stratum experiments -- 13.1.7 Order on association schemes -- 13.2 Algebra and combinatorics -- 13.2.1 Permutation groups, coherent con.guratons and cellular algebras -- 13.2.2 Strongly regular graphs -- 13.2.3 Distance-regular graphs -- 13.2.4 Geometry -- 13.2.5 Delsarte's thesis and coding theory -- 13.2.6 Duals -- 13.2.7 Imprimitivity -- 13.2.8 Recent work -- Glossary of notation -- References -- Index.