Combinatorics: Proceedings of the NATO Advanced Study Institute, Held at Nijenrode Castle, Breukelen, The Netherlands, 8-20 July 1974, Volume 1

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M. Hall Jr., J.H. van Lint
Taylor & Francis, Apr 30, 1975 - Mathematics - 482 pages
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Combinatorics has come of age. It had its beginnings in a number of puzzles which have still not lost their charm. Among these are EULER'S problem of the 36 officers and the KONIGSBERG bridge problem, BACHET's problem of the weights, and the Reverend T.P. KIRKMAN'S problem of the schoolgirls. Many of the topics treated in ROUSE BALL'S Recreational Mathe matics belong to combinatorial theory. All of this has now changed. The solution of the puzzles has led to a large and sophisticated theory with many complex ramifications. And it seems probable that the four color problem will only be solved in terms of as yet undiscovered deep results in graph theory. Combinatorics and the theory of numbers have much in common. In both theories there are many prob lems which are easy to state in terms understandable by the layman, but whose solution depends on complicated and abstruse methods. And there are now interconnections between these theories in terms of which each enriches the other. Combinatorics includes a diversity of topics which do however have interrelations in superficially unexpected ways. The instructional lectures included in these proceedings have been divided into six major areas: 1. Theory of designs; 2. Graph theory; 3. Combinatorial group theory; 4. Finite geometry; 5. Foundations, partitions and combinatorial geometry; 6. Coding theory. They are designed to give an overview of the classical foundations of the subjects treated and also some indication of the present frontiers of research.
 

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Contents

Constructions and Uses of Pairwise Balanced Designs
19
On Transversal Designs
43
On Finite NonCommutative Affine Spaces
65
Coding Theory
118
Weight Enumerators of Codes 115
141
Recent Results on Perfect Codes and Related Topics
163
Irreducible Cyclic Codes and Gauss Sums
185
Isomorphism Problems for Hypergraphs
205
Foundations Partitions and Combinatorial Geometry
261
Sperner Families and Partitions of a Partially Ordered
291
Combinatorial Reciprocity Theorems
307
Difference Sets
321
Invariant Relations Coherent Configurations
347
2Transitive Designs 365
413
Suborbits in Transitive Permutation Groups
419
Groups Polar Spaces and Related Structures
451

On an Extremal Property of Antichains in Partial
243
Applications of Ramsey Style Theorems to Eigenvalues
245

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Page 417 - Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62-89. MR 33 #5752.

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