Combinatorial Design Theory

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C.J. Colbourn, R. Mathon
Elsevier, Sep 22, 2011 - Mathematics - 469 pages
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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.

 

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Contents

Chapter 1 The Existence of Symmetric Latin Squares with One Prescribed Symbol in Each Row and Column
1
Chapter 2 A Fast Method for Sequencing Low Order NonAbelian Groups
27
Chapter 3 Pairwise Balanced Designs with Prime Power Block Sizes Exceeding 7
43
Chapter 4 Conjugate Orthogonal Latin Squares with EqualSized Holes
65
Chapter 5 On Regular Packings and Coverings
81
Chapter 6 An Inequality on the Parameters of Distance Regular Graphs and the Uniqueness of a Graph Related to M23
101
Chapter 7 Partitions into Indecomposable Triple Systems
107
Chapter 8 Cubic Neighbourhoods in Triple Systems
119
Chapter 22 A Product Theorem for Cyclic Graph Designs
287
Chapter 23 A New Class of Symmetric Divisible Designs
297
Chapter 24 225106 Designs Invariant under the Dihedral Group of Order Ten
301
Chapter 25 On the Steiner Systems S2425 Invariant under a Group of Order 9
307
Chapter 26 Simple 5286λ Designs from PSL 227
315
Chapter 27 The Existence of Partitioned Balanced Tournament Designs of Side 4n+3
319
Chapter 28 The Existence of Partitioned Balanced Tournament Designs
339
Chapter 29 Constructions for Cyclic Steiner 2Designs
353

Chapter 9 The Geometry of Subspaces of an Sλ23v
137
Chapter 10 On 3Blocking Sets in Projective Planes
145
Chapter 11 Star SubRamsey Numbers
153
Chapter 12 Colored Packing of Sets
165
Chapter 13 Balanced Room Squares from Finite Geometries and their Generalizations
179
Chapter 14 On the Number of Pairwise Disjoint Blocks in a Steiner System
189
Chapter 15 On Steiner Systems S3526
197
Chapter 16 Halving the Complete Design
207
Chapter 17 Outlines of Latin Squares
225
Chapter 18 The Flower Intersection Problem for Steiner Triple Systems
243
Chapter 19 Embedding Totally Symmetric Quasigroups
249
Chapter 20 Cyclic Perfect One Factorizations of K2n
259
Chapter 21 On Edge but not Vertex Transitive Regular Graphs
273
Chapter 30 On the Spectrum of Imbrical Designs
363
Chapter 31 Some Remarks on nClusters on Cubic Curves
371
Chapter 32 A Few More BIBDs with k 6 and λ 1
379
Chapter 33 Isomorphism Problems for Cyclic Block Designs
385
Chapter 34 Multiply Perfect Systems of Difference Sets
393
Chapter 35 Some Remarks on Focal Graphs
409
Chapter 36 Some Perfect OneFactorizations of K14
419
Chapter 37 A Construction for Orthogonal Designs with Three Variables
437
Chapter 38 Ismorphism Classes of Small Covering Designs with Block Size Five
441
Chapter 39 Graphs which are not Leaves of Maximal Partial Triple Systems
449
Chapter 40 Symmetric 2 31103 Designs with Automorphisms of Order Seven
461
Chapter 41 Embeddings of Steiner Systems S24v
465
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