Combinatorial Design Theory (eBook)

Front Cover 1
Combinatorial Design Theory 4
Copyright Page 5
Contents 10
Preface 6
Acknowledgements 8
Chapter 1. The Existence of Symmetric Latin Squares with One Prescribed Symbol in Each Row and Column 14
Chapter 2. A Fast Method for Sequencing Low Order Non-Abelian Groups 40
Chapter 3. Pairwise Balanced Designs with Prime Power Block Sizes Exceeding 7 56
Chapter 4. Conjugate Orthogonal Latin Squares with Equal-Sized Holes 78
Chapter 5. On Regular Packings and Coverings 94
Chapter 6. An Inequality on the Parameters of Distance Regular Graphs and the Uniqueness of a Graph Related to M23 114
Chapter 7. Partitions into Indecomposable Triple Systems 120
Chapter 8. Cubic Neighbourhoods in Triple Systems 132
Chapter 9. The Geometry of Subspaces of an S(. 2,3,v)
Chapter 10. On 3-Blocking Sets in Projective Planes 158
Chapter 11. Star Sub-Ramsey Numbers 166
Chapter 12. Colored Packing of Sets 178
Chapter 13. Balanced Room Squares from Finite Geometries and their Generalizations 192
Chapter 14. On the Number of Pairwise Disjoint Blocks in a Steiner System 202
Chapter 15. On Steiner Systems S(3,5,26) 210
Chapter 16. Halving the Complete Design 220
Chapter 17. Outlines of Latin Squares 238
Chapter 18. The Flower Intersection Problem for Steiner Triple Systems 256
Chapter 19. Embedding Totally Symmetric Quasigroups 262
Chapter 20. Cyclic Perfect One Factorizations of K2n 272
Chapter 21. On Edge but not Vertex Transitive Regular Graphs 286
Chapter 22. A Product Theorem for Cyclic Graph Designs 300
Chapter 23. A New Class of Symmetric Divisible Designs 310
Chapter 24. 2-(25,10,6) Designs Invariant under the Dihedral Group of Order Ten 314
Chapter 25. On the Steiner Systems S(2,4,25) Invariant under a Group of Order 9 320
Chapter 26. Simple 5-(28,6,.) Designs from PSL 2(27) 328
Chapter 27. The Existence of Partitioned Balanced Tournament Designs of Side 4n+3 332
Chapter 28. The Existence of Partitioned Balanced Tournament Designs 352
Chapter 29. Constructions for Cyclic Steiner 2-Designs 366
Chapter 30. On the Spectrum of Imbrical Designs 376
Chapter 31. Some Remarks on n-Clusters on Cubic Curves 384
Chapter 32. A Few More BIBD’s with k = 6 and . = 1 392
Chapter 33. Isomorphism Problems for Cyclic Block Designs 398
Chapter 34. Multiply Perfect Systems of Difference Sets 406
Chapter 35. Some Remarks on Focal Graphs 422
Chapter 36. Some Perfect One-Factorizations of K14 432
Chapter 37. A Construction for Orthogonal Designs with Three Variables 450
Chapter 38. Ismorphism Classes of Small Covering Designs with Block Size Five 454
Chapter 39. Graphs which are not Leaves of Maximal Partial Triple Systems 462
Chapter 40. Symmetric 2-( 31,10,3) Designs with Automorphisms of Order Seven 474
Chapter 41. Embeddings of Steiner Systems S(2,4,v) 478