Combinatorics '86

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M. Marchi, A. Barlotti, G. Tallini
Elsevier, Sep 22, 2011 - Mathematics - 501 pages
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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.

 

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Contents

Chapter 1 Net of Rationality in a Minkowski Plane
1
Chapter 2 A New Class of Translation Planes
7
Chapter 3 Quasigroups and Groups Arising from Cubic Surfaces
21
The Case
31
Chapter 5 Blocking Sets in the Projective Plane of Order Four
43
Chapter 6 Kalahari and the Sequence Sloane No 377
51
Chapter 7 Enciphered Geometry Some Applications of Geometry to Cryptography
59
Chapter 8 On Finite Grassmann Spaces
69
Chapter 30 Irreducible Representations of Hecke Algebras of Rank 2 Geometries
277
Chapter 31 A Characterization of Pappian Affine Hjelmslev Planes
281
Chapter 32 Embedding Locally Projective Planar Spaces in to Projective Spaces
293
Chapter 33 On Topological Incidence Groupoids
297
Chapter 34 Isomorphisms of Finite Hypergroupoids
301
Chapter 35 Seminversive Planes
311
Chapter 36 Geometric and Algebraic Methods in the Classification of Geometries Belonging to Lie Diagrams
315
Chapter 37 The ThasFisher Generalized Quadrangles
357

Chapter 9 The Regular Subgroups of the Sharply 3Transitive Finite Permutation Groups
75
Chapter 10 Hyperovals in Desarguesian Planes of Even Order
87
Chapter 11 Circular Block Designs from Planar NearRings
95
Chapter 12 Extending the Concept of Decomposability for Triple Systems
107
Chapter 13 Translation Partial Geometries
117
Chapter 14 On Admissible Sets with Two Intersection Numbers in a Projective PLane
137
Chapter 15 Commutative Finite AHypergroups of Length Two
147
Chapter 16 On Sets of Fixed Parity in Steiner Systems
157
Chapter 17 Blocking Sets of Index Two
169
Chapter 18 A Short Proof that Ordered Linear Spaces a r e Locally Projective
177
Chapter 19 Midpoints and Midlines in a Finite Hyperbolic Plane
181
Chapter 20 HallRyser Type Theorems for Relative Difference Sets
189
Chapter 21 Coordination of Generalized Quadrangles
195
Chapter 22 Construction of Some Planar Translation Spaces
209
Chapter 23 Regular Sets in Geometries
217
Chapter 24 Group Preserving Extensions of Skew Parabola Planes
225
Chapter 25 Products of Involutions in Orthogonal Groups
231
Chapter 26 Examples of Ovoidal MBbius Planes of Hering Class II1
249
Chapter 27 A Construction of Pairs and Triples of kIncomplete Orthogonal Arrays
251
Chapter 28 Relative Infinity in Projective De Sitter Spacetime and Its Relation to Proper Time
257
Chapter 29 Affine Hjelmslev Rings and Planes
265
Chapter 38 On Group Spaces Defined by Semidirect Products of Groups
367
Chapter 39 On Permutation Properties for Finitely Generated Semigroups
375
Chapter 40 On kSets of Type Omn in Srq with Three Exterior Hyperplanes
377
Chapter 41 An Algorithm for LS colourations
385
Chapter 42 A Blocking Set in PG 3 q q 5
391
Chapter 43 A Characterization of all Abelian Groups whose Lattice of Precompact Group Topologies Represents a Projective Geometry
395
Chapter 44 Groups of Homologies in 4Dimensional Stable Planes are Classical
399
Chapter 45 Polynomial Species and Connections among Bases of the Symmetric Polynomials
405
Chapter 46 Set and Sequence Closure for Finite Permutation Groups
413
Chapter 47 PCyclic Hypergroups with Three Characteristic Elements
421
Chapter 48 Order and Uniform Structure in Projective Geometry
427
Chapter 49 On Blocking Sets in Finite Projective and Affine Spaces
433
Chapter 50 Symmetric Designs without Ovals and Extremal SelfDual Codes
451
Chapter 51 Groups in Hypergroups
459
Chapter 52 The PerronFrobenius Projection in the Theory of Graphs Digraphs Designs and Stochastic Processes
469
Chapter 53 On the NonExistence of Certain Difference Sets
479
Chapter 54 On Complete 12Arcs i n Projective Planes of Order 12
485
Chapter 55 Block Designs Admitting Flag Transitive Groups of Automorphisms
493
Chapter 56 An Independence Theorem on the Conditions for Incidence Loops
497
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