Combinatorics '86 (eBook)

A. Barlotti, M. Marchi, G. Tallini (Herausgeber)

eBook Download: PDF

2011 | 1. Auflage
501 Seiten
Elsevier Science (Verlag)
978-0-08-086777-9 (ISBN)

Infos

Recent developments in all aspects of combinatorial and incidence geometry are covered in this volume, including their links with the foundations of geometry, graph theory and algebraic structures, and the applications to coding theory and computer science.

Topics covered include Galois geometries, blocking sets, affine and projective planes, incidence structures and their automorphism groups. Matroids, graph theory and designs are also treated, along with weak algebraic structures such as near-rings, near-fields, quasi-groups, loops, hypergroups etc., and permutation sets and groups.

The vitality of combinatorics today lies in its important interactions with computer science. The problems which arise are of a varied nature and suitable techniques to deal with them have to be devised for each situation, one of the special features of combinatorics is the often sporadic nature of solutions, stemming from its links with number theory. The branches of combinatorics are many and various, and all of them are represented in the 56 papers in this volume.

Inhalt

Front Cover 1
Combinatorics ’86 4
Copyright Page 5
Contens 10
Foreword 6
Opening Welcome 8
Participants 14
Chapter 1. Net of Rationality in a Minkowski Plane 18
Chapter 2. A New Class of Translation Planes 24
Chapter 3. Quasigroups and Groups Arising from Cubic Surfaces 38
Chapter 4. Blocking Sets in the Large Mathieu Designs, I: The Case 48
Chapter 5. Blocking Sets in the Projective Plane of Order Four 60
Chapter 6. Kalahari and the Sequence "Sloane No. 377" 68
Chapter 7. Enciphered Geometry. Some Applications of Geometry to Cryptography 76
Chapter 8. On Finite Grassmann Spaces 86
Chapter 9. The Regular Subgroups of the Sharply 3-Transitive Finite Permutation Groups 92
Chapter 10. Hyperovals in Desarguesian Planes of Even Order 104
Chapter 11. Circular Block Designs from Planar Near-Rings 112
Chapter 12. Extending the Concept of Decomposability for Triple Systems 124
Chapter 13. Translation Partial Geometries 134
Chapter 14. On Admissible Sets with Two Intersection Numbers in a Projective PLane 154
Chapter 15. Commutative Finite A-Hypergroups of Length Two 164
Chapter 16. On Sets of Fixed Parity in Steiner Systems 174
Chapter 17. Blocking Sets of Index Two 186
Chapter 18. A Short Proof that Ordered Linear Spaces a r e Locally Projective 194
Chapter 19. Midpoints and Midlines in a Finite Hyperbolic Plane 198
Chapter 20. Hall-Ryser Type Theorems for Relative Difference Sets 206
Chapter 21. Coordination of Generalized Quadrangles 212
Chapter 22. Construction of Some Planar Translation Spaces 226
Chapter 23. Regular Sets in Geometries 234
Chapter 24. Group Preserving Extensions of Skew Parabola Planes 242
Chapter 25. Products of Involutions in Orthogonal Groups 248
Chapter 26. Examples of Ovoidal MBbius Planes of Hering Class II1 266
Chapter 27. A Construction of Pairs and Triples of k-Incomplete Orthogonal Arrays 268
Chapter 28. Relative Infinity in Projective De Sitter Spacetime and Its Relation to Proper Time 274
Chapter 29. Affine Hjelmslev Rings and Planes 282
Chapter 30. Irreducible Representations of Hecke Algebras of Rank 2 Geometries 294
Chapter 31. A Characterization of Pappian Affine Hjelmslev Planes 298
Chapter 32. Embedding Locally Projective Planar Spaces in to Projective Spaces 310
Chapter 33. On Topological Incidence Groupoids 314
Chapter 34. Isomorphisms of Finite Hypergroupoids 318
Chapter 35. Seminversive Planes 328
Chapter 36. Geometric and Algebraic Methods in the Classification of Geometries Belonging to Lie Diagrams 332
Chapter 37. The Thas-Fisher Generalized Quadrangles 374
Chapter 38. On Group Spaces Defined by Semidirect Products of Groups 384
Chapter 39. On Permutation Properties for Finitely Generated Semigroups 392
Chapter 40. On k-Sets of Type (O,m,n) in Sr,q with Three Exterior Hyperplanes 394
Chapter 41. An Algorithm for LS -colourations 402
Chapter 42. A Blocking Set in PG ( 3 , q ) , q > = 5
Chapter 43. A Characterization of all Abelian Groups whose Lattice of Precompact Group Topologies Represents a Projective Geometry 412
Chapter 44. Groups of Homologies in 4-Dimensional Stable Planes are Classical 416
Chapter 45. Polynomial Species and Connections among Bases of the Symmetric Polynomials 422
Chapter 46. Set and Sequence Closure for Finite Permutation Groups 430
Chapter 47. P-Cyclic Hypergroups with Three Characteristic Elements 438
Chapter 48. Order and Uniform Structure in Projective Geometry 444
Chapter 49. On Blocking Sets in Finite Projective and Affine Spaces 450
Chapter 50. Symmetric Designs without Ovals and Extremal Self-Dual Codes 468
Chapter 51. Groups in Hypergroups 476
Chapter 52. The Perron-Frobenius Projection in the Theory of Graphs, Digraphs, Designs and Stochastic Processes 486
Chapter 53. On the Non-Existence of Certain Difference Sets 496
Chapter 54. On Complete 12-Arcs i n Projective Planes of Order 12 502
Chapter 55. Block Designs Admitting Flag Transitive Groups of Automorphisms 510
Chapter 56. An Independence Theorem on the Conditions for Incidence Loops 514

Produkt-Details

• Erscheint lt. Verlag: 22.9.2011
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Technik
• ISBN-10: 0-08-086777-4 / 0080867774
• ISBN-13: 978-0-08-086777-9 / 9780080867779