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Design Theory

C. C. Lindner and C. A. Rodger
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2009
Number of Pages: 
264
Format: 
Hardcover
Edition: 
2
Series: 
Discrete Mathematics and Its Applications 54
Price: 
89.95
ISBN: 
9781420082968
Category: 
Monograph
We do not plan to review this book.

 

Steiner Triple Systems 
The Existence Problem
v ≡ 3 (mod 6): The Bose Construction
v ≡ 1 (mod 6): The Skolem Construction
v ≡ 5 (mod 6): The 6n + 5 Construction
Quasigroups with Holes and Steiner Triple Systems
The Wilson Construction
Cyclic Steiner Triple Systems
The 2n + 1 and 2n + 7 Constructions
λ-Fold Triple Systems 
Triple Systems of Index λ > 1
The Existence of Indempotent Latin Squares
2-fold Triple Systems
λ = 3 and 6
λ-Fold Triple Systems in General
Quasigroup Identities and Graph Decompositions 
Quasigroup Identities
Mendelsohn Triple Systems Revisited
Steiner Triple Systems Revisited
Maximum Packings and Minimum Coverings 
The General Problem
Maximum Packings
Minimum Coverings
Kirkman Triple Systems
A Recursive Construction
Constructing Pairwise Balanced Designs
Mutually Orthogonal Latin Squares 
Introduction
The Euler and MacNeish Conjectures
Disproof of the MacNeish Conjecture
Disproof of the Euler Conjecture
Orthogonal Latin Squares of Order n ≡ 2 (mod 4)
Affine and Projective Planes 
Affine Planes
Projective Planes
Connections between Affine and Projective Planes
Connection between Affine Planes and Complete Sets of MOLS
Coordinating the Affine Plane
Intersections of Steiner Triple Systems 
Teirlinck’s Algorithm
The General Intersection Problem
Embeddings
Embedding Latin Rectangles—Necessary Conditions
Edge-Coloring Bipartite Graphs
Embedding Latin Rectangles: Ryser’s Sufficient Conditions
Embedding Idempotent Commutative Latin Squares: Cruse’s Theorem
Embedding Partial Steiner Triple Systems
Steiner Quadruple Systems
Introduction
Constructions of Steiner Quadruple Systems
The Stern and Lenz Lemma
The (3v – 2u)-Construction
Appendix A: Cyclic Steiner Triple Systems
Appendix B: Answers to Selected Exercises
References
Index

Dummy View - NOT TO BE DELETED