Freshly Printed - allow 10 days lead
Couldn't load pickup availability
Latin Squares and their Applications
This is a comprehensive revision of the definitive text on latin squares and related topics
A. Donald Keedwell (Author), József Dénes (Author)
9780444635556, Elsevier Science
Hardback, published 24 July 2015
438 pages
22.9 x 15.1 x 2.8 cm, 0.82 kg
"This book is a comprehensive account of the subject of latin squares (and latin rectangles), by two experts. The book is written in a fairly condensed but readable ‘narrative style’. It is packed with information, either expounded in detail or with full references to the literature." --The Mathematical Gazette "...an in-depth summary of the extensive research about Latin Squares. I now have a possible new research direction that can provide many questions for undergraduates and the book will be a good resource in the future." --MAA Reviews "A reader looking for an updated presentation of some topics from the 1974 book can find much of value in the present volume." - Mathematical Reviews
Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties.
1. Elementary properties 2. Special types of latin square 3. Partial latin squares and partial transversals4. Classification and enumeration of latin squares and latin rectangles5. The concept of orthogonality6. Connections between latin squares and magic squares7. Constructions of orthogonal latin squares which involve re-arrangement of rows and columns 8. Connections with geometry and graph theory 9. Latin squares with particular properties 10. Alternative versions of orthogonality11. Miscellaneous topics AppendicesThe present state of the problems New problems
Subject Areas: Discrete mathematics [PBD]
