Created to teach students many of the most important techniques used 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.
Rezensionen / Stimmen
Design Theory is exploring an area in combinatorics that concerns the conditions for existence of several important block designs and methods to construct them. It explains these techniques in good detail and accompanies the theory with helpful illustrations that serve their purpose admirably. The material of this book has been carefully ordered and results, theorems and constructions build successively on previously presented definitions and explanations ... a helpful addition to any combinatorist's library and provides a nice introduction to block design construction techniques, with a collection of carefully selected and effectively presented topics.
-Dimitris Papamichail, SIGACT News, December 2011
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 235 mm
Breite: 156 mm
Gewicht
ISBN-13
978-0-8493-3986-8 (9780849339868)
Schweitzer Klassifikation
Steiner Triple Systems
The Existence Problem
u ? 3 (mod 6): The Bose Construction
u ? 1 (mod 6): The Skolem Construction
u ? 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
l-Fold Triple Systems
Triple Systems of Index l > 1
The Existence of Idempotent Latin Squares
2-Fold Triple Systems
Constructing 2-Fold Triple Systems
l = 3 and 6
l-Fold Triple Systems in General
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
Connections between Affine Planes and Complete Sets of MOLS (n)
Coordinating the Affine Planes
Steiner Quadruple Systems
Introduction
Constructions of Steiner Quadruple Systems
The Stern and Lenz Lemma
The (3u - 2u)-Construction
Appendices
A. Cyclic Steiner Triple Systems
B. Answers to Selected Exercises
Index
