Algebraic and Geometric Combinatorics (eBook)

Front Cover 1
Algebraic and Geometric Combinatorics 4
Copyright Page 5
Contents 13
Nathan Saul Mendelsohn 8
Nathan Mendelsohn As I have known him 10
Editor's preface 12
Chapter 1. On hamiltonian cycles in metacirculant graphs 16
Chapter 2. Embedding latin squares with prescribed diagonal 24
Chapter 3. A direct construction for latin squares without proper subsquares 42
Chapter 4. High chromatic rigid graphs II 70
Chapter 5. Direct constructions for perfect 3-cyclic designs 78
Chapter 6. Distance-regular graphs with diameter three 84
Chapter 7. Colour schemes 96
Chapter 8. The analysis of directed triple systems by refinement 112
Chapter 9. On the product of all elements in a finite group 120
Chapter 10. Enumeration of symmetric designs (25,9,3) 126
Chapter 11. On pairwise balanced block designs with the sizes of blocks as uniform as possible 144
Chapter 12. Finite representations of two-variable identities or why are finite fields important in combinatorics ? 150
Chapter 13. Some connections between Steiner systems and self-conjugate sets of M.O.L.S. 158
Chapter 14. Incidence-geometric aspects of finite abelian groups 176
Chapter 15. Two remarks on the Mendelsohn-Dulmage theorem 186
Chapter 16. Düroids 194
Chapter 17. Lattice polyhedra II: Generalization, construction and examples 204
Chapter 18. A partial geometry pg (9, 8, 4) 220
Chapter 19. Homomorphism interpolation and approximation 228
Chapter 20. Prolongation in m -dimensional permutation cubes 244
Chapter 21. Match-tables 254
Chapter 22. On the sequenceability of dihedral groups 268
Chapter 23. A combinatorial construction of the small Mathieu designs and groups 274
Chapter 24. Embeddings and prescribed intersections of transitive triple systems 280
Chapter 25. Simple Steiner quadruple systems 308
Chapter 26. On linked arrays of pairs 288
Chapter 27. Rectagraphs, diagrams, and Suzuki’s sporadic simple group 320
Chapter 28. Logic of equality in geometry 334
Chapter 29. On axial automorphisms of symmetric designs 348
Chapter 30. Pictures in lattice theory 356
Chapter 31. On mutually orthogonal resolutions and near-resolutions 372
Appendix. Research papers by N.S. Mendelsohn 386