Combinatorial Design Theory
Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science. This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the curre
eBook, English, 2014
Elsevier Science, Amsterdam, 2014
1 online resource (483 pages)
9780080872605, 0080872603
1048594109
Front Cover; Combinatorial Design Theory; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. The Existence of Symmetric Latin Squares with One Prescribed Symbol in Each Row and Column; Chapter 2. A Fast Method for Sequencing Low Order Non-Abelian Groups; Chapter 3. Pairwise Balanced Designs with Prime Power Block Sizes Exceeding 7; Chapter 4. Conjugate Orthogonal Latin Squares with Equal-Sized Holes; Chapter 5. On Regular Packings and Coverings; Chapter 6. An Inequality on the Parameters of Distance Regular Graphs and the Uniqueness of a Graph Related to M23. Chapter 7. Partitions into Indecomposable Triple SystemsChapter 8. Cubic Neighbourhoods in Triple Systems; Chapter 9. The Geometry of Subspaces of an S(n; 2,3,v); Chapter 10. On 3-Blocking Sets in Projective Planes; Chapter 11. Star Sub-Ramsey Numbers; Chapter 12. Colored Packing of Sets; Chapter 13. Balanced Room Squares from Finite Geometries and their Generalizations; Chapter 14. On the Number of Pairwise Disjoint Blocks in a Steiner System; Chapter 15. On Steiner Systems S(3,5,26); Chapter 16. Halving the Complete Design; Chapter 17. Outlines of Latin Squares. Chapter 18. The Flower Intersection Problem for Steiner Triple SystemsChapter 19. Embedding Totally Symmetric Quasigroups; Chapter 20. Cyclic Perfect One Factorizations of K2n; Chapter 21. On Edge but not Vertex Transitive Regular Graphs; Chapter 22. A Product Theorem for Cyclic Graph Designs; Chapter 23. A New Class of Symmetric Divisible Designs; Chapter 24. 2-(25,10,6) Designs Invariant under the Dihedral Group of Order Ten; Chapter 25. On the Steiner Systems S(2,4,25) Invariant under a Group of Order 9; Chapter 26. Simple 5-(28,6, n) Designs from PSL 2(27). Chapter 27. The Existence of Partitioned Balanced Tournament Designs of Side 4n+3Chapter 28. The Existence of Partitioned Balanced Tournament Designs; Chapter 29. Constructions for Cyclic Steiner 2-Designs; Chapter 30. On the Spectrum of Imbrical Designs; Chapter 31. Some Remarks on n-Clusters on Cubic Curves; Chapter 32. A Few More BIBD's with k = 6 and n = 1; Chapter 33. Isomorphism Problems for Cyclic Block Designs; Chapter 34. Multiply Perfect Systems of Difference Sets; Chapter 35. Some Remarks on Focal Graphs; Chapter 36. Some Perfect One-Factorizations of K14. Chapter 37. A Construction for Orthogonal Designs with Three VariablesChapter 38. Ismorphism Classes of Small Covering Designs with Block Size Five; Chapter 39. Graphs which are not Leaves of Maximal Partial Triple Systems; Chapter 40. Symmetric 2-(31,10,3) Designs with Automorphisms of Order Seven; Chapter 41. Embeddings of Steiner Systems S(2,4,v)