Keedwell's Latin Squares and Their Applications, Second Edition, offers a long-awaited update and reissue of this seminal literature. The revision retains foundational, original material from the highly-cited 1974 volume, 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. Condensing areas which are no longer the focus of new research, the book expands upon active and emerging areas. Returning to the 73 Unsolved Problems included with commentary in the first edition, this update reviews the current knowledge base about those as well as new problems. Through an engaging narrative, Latin Squares and Their Applications, Second Edition, provides thorough coverage of the topic, one of the oldest of all discrete mathematical structures, as well as one of the most relevant. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they describe the order in which to apply different experimental treatments to expedite the statistical analysis of their efficacy; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. Retains the organization and updated foundational material from the original edition, explores current and emerging research topicsIncludes the original 73 Unsolved Problems with the current understanding of them, as well as new Unsolved Problems for further consideration and studyCorrected and improved content with recommendations and contributions from leading researcher Ian Wanless INDICE: Chapter 1. Elementary properties Chapter 2. Special types of latin square Chapter 3. Partial latin squares and partial transversals Chapter 4. Classification and enumeration of latin squares and latin rectangles Chapter 5. The concept of orthogonality Chapter 6. Connections between latin squares and magic squares Chapter 7. Constructions of orthogonal latin squares which involve re-arrangement of rows and columns Chapter 8. Connections with geometry and graph theory Chapter 9. Latin squares with particular properties Chapter 10. Alternative versions of orthogonality Chapter 11. Miscellaneous topics Appendices: The present state of the problems New problems Bibliography and author index Subject index
- ISBN: 978-0-444-63555-6
- Editorial: North Holland
- Encuadernacion: Cartoné
- Páginas: 438
- Fecha Publicación: 27/07/2015
- Nº Volúmenes: 1
- Idioma: Inglés