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Combinatorics

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

  • Conference proceedings
  • © 1975

Overview

Editors:
  1. M. Hall
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  2. J. H. Lint
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Part of the book series: Nato Science Series C: (ASIC, volume 16)

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Table of contents (21 papers)

  1. Front Matter

    Pages I-VIII
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  2. Part 1

    1. Front Matter

      Pages 1-1
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    2. Theory of Designs

      1. Indeterminates and Incidence Matrices
        • H. J. Ryser
        Pages 3-17
      2. Constructions and Uses of Pairwise Balanced Designs
        • R. M. Wilson
        Pages 19-42
      3. On Transversal Designs
        • H. Hanani
        Pages 43-53

    3. Finite Geometry

      1. Combinatorics of Finite Geometries
        • A. Barlotti
        Pages 55-63
      2. On Finite Non-Commutative Affine Spaces
        • J. André
        Pages 65-113

    4. Coding Theory

      1. Weight Enumerators of Codes
        • N. J. A. Sloane
        Pages 115-142
      2. The Association Schemes of Coding Theory
        • P. Delsarte
        Pages 143-161
      3. Recent Results on Perfect Codes and Related Topics
        • J. H. Van Lint
        Pages 163-183
      4. Irreducible Cyclic Codes and Gauss Sums
        • R. J. McEliece
        Pages 185-202

  3. Part 2

    1. Front Matter

      Pages 203-203
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    2. Graph Theory

      1. Isomorphism Problems for Hypergraphs
        • C. Berge
        Pages 205-214
      2. Extremal Problems for Hypergraphs
        • G. O. H. Katona
        Pages 215-244
      3. Applications of Ramsey Style Theorems to Eigenvalues of Graphs
        • A. J. Hoffman
        Pages 245-259

    3. Foundations, Partitions and Combinatorial Geometry

      1. Some Recent Developments in Ramsey Theory
        • R. L. Graham, B. L. Rothschild
        Pages 261-276
      2. On An Extremal Property of Antichains in Partial Orders. The Lym Property and Some of Its Implications and Applications
        • D. J. Kleitman
        Pages 277-290
      3. Sperner Families and Partitions of A Partially Ordered Set
        • C. Greene
        Pages 291-306
      4. Combinatorial Reciprocity Theorems
        • R. P. Stanley
        Pages 307-318

  4. Part 3

    1. Front Matter

      Pages 319-319
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Combinatorics

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

  • Editors: M. Hall, J. H. Lint

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-010-1826-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Mathematical Centre, Amsterdam 1975

  • Hardcover ISBN: 978-90-277-0593-8Due: 30 April 1975

  • eBook ISBN: 978-94-010-1826-5Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: VIII, 482

  • Topics: Combinatorics

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