Discrete mathematics using Latin squares.

*(English)*Zbl 0957.05002
Wiley-Interscience Series in Discrete Mathematics and Optimization. New York, NY: Wiley. xv, 305 p. (1998).

The authors employ the common thread of Latin squares to allow them to weave together many important areas of discrete mathematics. Their book is suitable as a text for advanced undergraduate students. Although topics of importance from linear algebra and abstract algebra are provided when needed, the maturity gained from having studied those subjects would prove invaluable in reaping the most benefit from this very well-written and interesting text.

After an introduction to Latin squares and a discussion of mutually orthogonal Latin squares, the authors present various generalizations (orthogonal hypercubes and frequency squares). They then present related topics from discrete mathematics, covering the inclusion-exclusion principle, groups, and graphs, showing their relationships with Latin squares. Applications to affine and projective planes, combinatorial designs, magic squares, Room squares, statistics, error-correcting codes, cryptology, and nets are dealt with in detail.

After the introductory chapters, most of the chapters are completely independent of each other, and so a number of different types of courses could be offered from this book. Exercises with hints and partial solutions, and many references, are included.

After an introduction to Latin squares and a discussion of mutually orthogonal Latin squares, the authors present various generalizations (orthogonal hypercubes and frequency squares). They then present related topics from discrete mathematics, covering the inclusion-exclusion principle, groups, and graphs, showing their relationships with Latin squares. Applications to affine and projective planes, combinatorial designs, magic squares, Room squares, statistics, error-correcting codes, cryptology, and nets are dealt with in detail.

After the introductory chapters, most of the chapters are completely independent of each other, and so a number of different types of courses could be offered from this book. Exercises with hints and partial solutions, and many references, are included.

Reviewer: Chester J.Salwach (Easton)