Design TheoryCreated 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. |
Contents
Steiner Triple Systems | 1 |
Maximum Packings and Minimum Coverings | 53 |
Mutually Orthogonal Latin Squares | 83 |
Affine and Projective Planes | 131 |
Steiner Quadruple Systems | 145 |
A Cyclic Steiner Triple Systems | 187 |
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Common terms and phrases
1-factorization 2-fold triple system 2v Construction 3-element subsets affine plane B₁ base blocks block of size block sizes Bose Construction cell complete graph containing the triple contains a SQS(8 contains symbol covering of order deficiency graph Euler Conjecture Exercise exists Figure find the triple finite field following triples holes H idempotent quasigroup Kirkman triple system MacNeish Conjecture maximum packing minimum covering mod g modulo number of triples order 12 order 2n ordered pair orthogonal latin squares orthogonal quasigroups packing of order pair of orthogonal pair of symbols parallel class partition PBD of order plane of order projective plane quadruples in Q1 quasigroup of order quasigroup with holes rename the symbols S. S. Shrikhande set of MOLS(n Skolem Construction SQS(u SQS(v squares of order Steiner Quadruple System Steiner triple system STS(v system of order triples containing Type 1 quadruples Type 2 triples X-fold