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Combinatorics

Proceedings of the NATO Advanced Study Institute held at Nijenrode Castle, Breukelen, The Netherlands 8–20 July 1974

  • Editors
  • M. HallJr.
  • J. H. van Lint

Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 16)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Part 1

    1. Front Matter
      Pages 1-1
    2. Theory of Designs

      1. H. J. Ryser
        Pages 3-17
      2. H. Hanani
        Pages 43-53
    3. Finite Geometry

      1. A. Barlotti
        Pages 55-63
    4. Coding Theory

      1. N. J. A. Sloane
        Pages 115-142
      2. P. Delsarte
        Pages 143-161
      3. R. J. McEliece
        Pages 185-202
  3. Part 2

    1. Front Matter
      Pages 203-203
    2. Graph Theory

    3. Foundations, Partitions and Combinatorial Geometry

  4. Part 3

    1. Front Matter
      Pages 319-319
    2. Combinatorial Group Theory

      1. M. Hall Jr.
        Pages 321-346
      2. W. M. Kantor
        Pages 365-418
      3. P. J. Cameron
        Pages 419-450

About these proceedings

Introduction

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.

Keywords

Combinatorics Graph theory Hypergraph Partition Permutation Ramsey theory combinatorial geometry graphs

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-1826-5
  • Copyright Information Springer Science+Business Media B.V. 1975
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-1828-9
  • Online ISBN 978-94-010-1826-5
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site