| |
| |
| |
| Steiner Triple Systems | |
| |
| |
| |
| The existence problem | |
| |
| |
| |
| v [identical with] 3 (mod 6): The Bose Construction | |
| |
| |
| |
| v [identical with] 1 (mod 6): The Skolem Construction | |
| |
| |
| |
| v [identical with] 5 (mod 6): The 6n + 5 Construction | |
| |
| |
| |
| Quasigroups with holes and Steiner triple systems | |
| |
| |
| |
| Constructing quasigroups with holes | |
| |
| |
| |
| Constructing Steiner triple systems using quasigroups with holes | |
| |
| |
| |
| The Wilson Construction | |
| |
| |
| |
| Cyclic Steiner triple systems | |
| |
| |
| |
| The 2n + 1 and 2n + 7 Constructions | |
| |
| |
| |
| [lambda]-Fold Triple Systems | |
| |
| |
| |
| Triple systems of index [lambda] > 1 | |
| |
| |
| |
| The existence of idempotent latin squares | |
| |
| |
| |
| 2-Fold triple systems | |
| |
| |
| |
| Constructing 2-fold triple systems | |
| |
| |
| |
| Mendelsohn triple systems | |
| |
| |
| |
| [lambda] = 3 and 6 | |
| |
| |
| |
| [lambda]-Fold triple systems in general | |
| |
| |
| |
| Quasigroup Identities and Graph Decompositions | |
| |
| |
| |
| Quasigroup identities | |
| |
| |
| |
| Mendelsohn triple systems revisited | |
| |
| |
| |
| Steiner triple systems revisited | |
| |
| |
| |
| Maximum Packings and Minimum Coverings | |
| |
| |
| |
| The general problem | |
| |
| |
| |
| Maximum packings | |
| |
| |
| |
| Minimum coverings | |
| |
| |
| |
| Kirkman Triple Systems | |
| |
| |
| |
| A recursive construction | |
| |
| |
| |
| Constructing pairwise balanced designs | |
| |
| |
| |
| Mutually Orthogonal Latin Squares | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Euler and MacNeish Conjectures | |
| |
| |
| |
| Disproof of the MacNeish Conjecture | |
| |
| |
| |
| Disproof of the Euler Conjecture | |
| |
| |
| |
| Orthogonal latin squares of order n [identical with] 2 (mod 4) | |
| |
| |
| |
| Affine and Projective Planes | |
| |
| |
| |
| Affine planes | |
| |
| |
| |
| Projective planes | |
| |
| |
| |
| Connections between affine and projective planes | |
| |
| |
| |
| Connection between affine planes and complete sets of MOLS | |
| |
| |
| |
| Coordinatizing the affine plane | |
| |
| |
| |
| Intersections of Steiner Triple Systems | |
| |
| |
| |
| Teirlinck's Algorithm | |
| |
| |
| |
| The general intersection problem | |
| |
| |
| |
| Embeddings | |
| |
| |
| |
| Embedding latin rectangles - necessary conditions | |
| |
| |
| |
| Edge-coloring bipartite graphs | |
| |
| |
| |
| Embedding latin rectangles: Pyser's Sufficient Conditions | |
| |
| |
| |
| Embedding idempotent communtative latin squares: Cruse's Theorem | |
| |
| |
| |
| Embedding partial Steiner triple systems | |
| |
| |
| |
| Steiner Quadruple Systems | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Constructions of Steiner Quadruple Systems | |
| |
| |
| |
| The Stern and Lenz Lemma | |
| |
| |
| |
| The (3v - 2u)-Construction | |
| |
| |
| Appendices | |
| |
| |
| |
| Cyclic Steiner Triple Systems | |
| |
| |
| |
| Answers to Selected Exercises | |
| |
| |
| References | |
| |
| |
| Index | |