Design Theory

ISBN-10: 1420082965

ISBN-13: 9781420082968

Edition: 2nd 2011 (Revised)

List price: $104.95
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Description:

Important and Exciting Construction Design Techniques The second edition of a basic text on design theory, this book examines some of the most important techniques used for constructing combinatorial designs. Focusing on several basic designs such as Steiner Triple Systems, Latin Squares, and finite projective and affine planes, the authors add interesting properties such as resolvability and orthogonality. This new edition adds material on embedding designs, algorithms for producing disjoint designs, and algebraic connections between quasigroups and graph decompositions. In addition, several of the more complicated structures, such as the Steiner quadruple systems are also included. The book is supplemented with problem sets and examples.
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Book details

List price: $104.95
Edition: 2nd
Copyright year: 2011
Publisher: CRC Press LLC
Publication date: 10/23/2008
Binding: Hardcover
Pages: 272
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 1.342
Language: English

Steiner Triple Systems
The existence problem
v [identical with] 3 (mod 6): The Bose Construction
v [identical with] 1 (mod 6): The Skolem Construction
v [identical with] 5 (mod 6): The 6n + 5 Construction
Quasigroups with holes and Steiner triple systems
Constructing quasigroups with holes
Constructing Steiner triple systems using quasigroups with holes
The Wilson Construction
Cyclic Steiner triple systems
The 2n + 1 and 2n + 7 Constructions
[lambda]-Fold Triple Systems
Triple systems of index [lambda] > 1
The existence of idempotent latin squares
2-Fold triple systems
Constructing 2-fold triple systems
Mendelsohn triple systems
[lambda] = 3 and 6
[lambda]-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 [identical with] 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
Coordinatizing 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: Pyser's Sufficient Conditions
Embedding idempotent communtative 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
Appendices
Cyclic Steiner Triple Systems
Answers to Selected Exercises
References
Index
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