Combinatorial Design Theory

C.J. Colbourn, R. Mathon

• Publisher: North Holland
• Year: 2011
• Print ISBN:
  9780444703286
• eBook ISBN:
  9780080872605
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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 current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions.The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.

Table of contents

• 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 Systems
• Chapter 8. Cubic Neighbourhoods in Triple Systems
• Chapter 9. The Geometry of Subspaces of an S(λ;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 Systems
• Chapter 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,λ) Designs from PSL 2(27)
• Chapter 27. The Existence of Partitioned Balanced Tournament Designs of Side 4n+3
• Chapter 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 λ = 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 Variables
• Chapter 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)