Topics on Steiner Systems (eBook)

Front Cover 1
Topics on Steiner System 4
Copyright Page 5
Contents 9
Preface 6
From the Editors 8
Part I: Algebraic aspects of Steiner systems 12
Chapter 1. Co-ordinatizing Steiner systems 14
Chapter 2. Algebraic speculations about Steiner systems 36
Chapter 3. Almost all Steiner triple systems are asymmetric 48
Part II: Steiner systems with higher value of t 52
Chapter 4. External results and configuration theorems for Steiner systems 54
Chapter 5. The problem of the higher values of t 76
Part III: Steiner systems with given properties, collections of Steiner systems, and their relationship to other combinatorial configurations 82
Chapter 6. Dimension in Steiner triple systems 84
Chapter 7. Perpendicular arrays of triple systems 100
Chapter 8. Steiner systems and Room squares 106
Chapter 9. A survey of derived triple systems 116
Chapter 10. Intersection properties of Steiner systems 126
Part IV: Resolvability and embedding problems for Steiner systems 140
Chapter 11. On identifying PG(3,2) and the complete 3-design on seven points 142
Chapter 12. A survey on resolvable quadruple systems 154
Chapter 13. Projective embeddings of small "Steiner Triple systems" 162
Chapter 14. A survey of embedding theorems for Steiner systems 186
Chapter 15. On the size of partial parallel classes in Steiner systems 214
Part V: Isomorphism problems and enumeration of Steiner systems 224
Chapter 16. On cyclic Steiner 2-designs 226
Chapter 17. Non-isomorphic reverse Steiner triple systems of order 19 266
Chapter 18. An enumeration method for non- isomorphic combinatorial designs 276
Chapter 19. On cyclic Steiner systems S(3, 4, 20) 288
Chapter 20. On cyclic Steiner systems S(3, 4, 22) 312
Part VI: Bibliography and survey of Steiner systems 326
Chapter 21. An updated bibliography and survey of Steiner systems 328