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Latin squares and their applications /
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 autho...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
Elsevier,
2015.
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Latin Squares and their Applications; Copyright; Foreword to the First Edition; Contents; Preface to the First Edition; Acknowledgements (First Edition); Preface to the Second Edition; Chapter 1: Elementary Properties; 1.1 The Multiplication Table of a Quasigroup; 1.2 The Cayley Table of a Group; 1.3 Isotopy; 1.4 Conjugacy and Parastrophy; 1.5 Transversals and Complete Mappings; 1.6 Latin Subsquares and Subquasigroups; Chapter 2: Special Types of Latin Square; 2.1 Quasigroup Identities and Latin Squares.
- 2.2 Quasigroups of Some Special Types and the Concept of Generalized Associativity2.3 Triple Systems and Quasigroups; 2.4 Group-Based Latin Squares and Nuclei of Loops; 2.5 Transversals in Group-Based Latin Squares; 2.6 Complete Latin Squares; Chapter 3: Partial Latin Squares and Partial Transversals; 3.1 Latin Rectangles and Row Latin Squares; 3.2 Critical Sets and Sudoku Puzzles; 3.3 Fuchs' Problems; 3.4 Incomplete Latin Squares and Partial Quasigroups; 3.5 Partial Transversals and Generalized Transversals; Chapter 4: Classification and Enumeration of Latin Squares and Latin Rectangles.
- 4.1 The Autotopism Group of a Quasigroup4.2 Classification of Latin Squares; 4.3 History of the Classification and Enumeration of Latin Squares; 4.4 Enumeration of Latin Rectangles; 4.5 Enumeration of Transversals; 4.6 Enumeration of Subsquares; Chapter 5: The Concept of Orthogonality; 5.1 Existence Questions for Incomplete Sets of Orthogonal Latin Squares; 5.2 Complete Sets of Orthogonal Latin Squares and Projective Planes; 5.3 Sets of MOLS of Maximum and Minimum Size; 5.4 Orthogonal Quasigroups, Qroupoids and Triple Systems.
- 5.5 Self-Orthogonal and Other Parastrophic Orthogonal Latin Squares and Quasigroups5.6 Orthogonality in Other Structures Related to Latin Squares; Chapter 6: Connections Between Latin Squares and Magic Squares; 6.1 Diagonal (or Magic) Latin Squares; 6.2 Construction of Magic Squares with the Aid of Orthogonal Latin Squares.; 6.3 Additional Results on Magic Squares; 6.4 Room Squares: Their Construction and Uses; Chapter 7: Constructions of Orthogonal Latin Squares Which Involve Rearrangement of Rows and Columns; 7.1 Generalized Bose Construction: Constructions Based on Abelian Groups.
- 7.2 The Automorphism Method of H.B. Mann7.3 The Construction of Pairs of Orthogonal Latin Squares of Order Ten; 7.4 The Column Method; 7.5 The Diagonal Method; 7.6 Left Neofields and Orthomorphisms of Groups; Chapter 8: Connections with Geometry and Graph Theory; 8.1 Quasigroups and 3-Nets; 8.2 Orthogonal Latin Squares, k-Nets and Introduction of Co-ordinates; 8.3 Latin Squares and Graphs; Chapter 9: Latin Squares with Particular Properties; 9.1 Bachelor Squares; 9.2 Homogeneous Latin Squares; 9.3 Diagonally Cyclic Latin Squares and Parker Squares.