Design Theory / Edition 1

Design Theory / Edition 1

by Charles C. Lindner, Christopher A. Rodger, Charles C. Kindner
     
 

ISBN-10: 0849339863

ISBN-13: 9780849339868

Pub. Date: 06/25/1997

Publisher: Taylor & Francis

Created to teach students many of the most important techniquesused for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in Combinatorial Design Theory. The text features clear explanations of basic designs such as Steiner and Kirkman triple systems, mutually orthogonal Latin squares, finite projective and

Overview

Created to teach students many of the most important techniquesused for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in Combinatorial Design Theory. The text features clear explanations of basic designs such as Steiner and Kirkman triple systems, mutually orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well prepared to construct a vast array of combinatorial designs.

Design Theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas, or that reinforces and builds upon similar ideas previously introduced. The many illustrations aid in understanding and enjoying the application of the constructions described. Written by professors with the needs of students in mind, this is destined to become the standard textbook for design theory.

Product Details

ISBN-13:
9780849339868
Publisher:
Taylor & Francis
Publication date:
06/25/1997
Series:
Discrete Mathematics and Its Applications Series, #6
Edition description:
Older Edition
Pages:
208
Product dimensions:
6.41(w) x 9.58(h) x 0.66(d)

Table of Contents

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

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