Design Theory 2nd edition [Kietas viršelis]

In order to teach students some of the most important techniques used for constructing combinatorial designs, Lindner and Rodger (both Auburn U.) focus on several basic designs: Steiner triple systems, latin squares, and finite projective and affine plane. Having set these out, they start to add additional interesting properties that may be required, such as resolvability, embeddings, orthogonality, and even some more complicated structures such as Steiner quadruple systems. They do not mention a date for the first edition, but have added extensive material introducing embeddings, directed designs, the universal algebraic representations of designs, and intersection properties of designs. Check out their pictures, they say, which make the constructions more comprehensible to students. Answers are provided for selected problems. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)

Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics.

This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs.

The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems.

By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.