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Higher Combinatorics

Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1–10, 1976

  • Conference proceedings
  • © 1977

Overview

Editors:
  1. Martin Aigner

    1. Fachbereich Mathematik, Freie Universität Berlin, Berlin 33, Germany

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Part of the book series: Nato Science Series C: (ASIC, volume 31)

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Table of contents (16 papers)

  1. Front Matter

    Pages I-XIII
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  2. Counting Theory

    1. Front Matter

      Pages 1-1
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    2. Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials

      • George E. Andrews, Richard Askey
      Pages 3-26

    3. Distributions Euleriennes et Mahoniennes sur le Groupe des Permutations

      • Dominique Foata
      Pages 27-49

    4. Cohen-Macaulay Complexes

      • Richard P. Stanley
      Pages 51-62

  3. Combinatorial Set Theory and Order Theory

    1. Front Matter

      Pages 63-63
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    2. Acyclic Orientations

      • Martin Aigner
      Pages 65-68

    3. Problems in Combinatorial Set Theory

      • Richard Rado
      Pages 69-78

    4. Aspects of Finite Lattices

      • R. Wille
      Pages 79-100

  4. Matroids

    1. Front Matter

      Pages 101-101
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    2. Geometries Associated with Partially Ordered Sets

      • T. A. Dowling, W. A. Denig
      Pages 103-116

    3. Transversal Matroids and Related Structures

      • A. W. Ingleton
      Pages 117-131

    4. Matroids as the Study of Geometrical Configurations

      • J. H. Mason
      Pages 133-176

  5. Designs

    1. Front Matter

      Pages 177-177
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    2. Partitions of X2 and Other Topics

      • Martin Aigner
      Pages 179-181

    3. Combinatorics of Partial Geometries and Generalized Quadrangles

      • J. A. Thas
      Pages 183-199

    4. Edge Decompositions of Colored Graphs

      • Martin Aigner
      Pages 201-202

  6. Group and Coding Theory

    1. Front Matter

      Pages 203-203
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    2. Planes and Biplanes

      • E. F. Assmus Jr., Joseph A. Mezzaroba, Chester J. Salwach
      Pages 205-212

    3. Ovals from the Point of View of Coding Theory

      • E. F. Assmus Jr., Howard E. Sachar
      Pages 213-216
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Keywords

About this book

It is general consensus that Combinatorics has developed into a full-fledged mathematical discipline whose beginnings as a charming pastime have long since been left behind and whose great signifi­ cance for other branches of both pure and applied mathematics is only beginning to be realized. The last ten years have witnessed a tremendous outburst of activity both in relatively new fields such as Coding Theory and the Theory of Matroids as well as in' more time honored endeavors such as Generating Functions and the Inver­ sion Calculus. Although the number of text books on these subjects is slowly increasing, there is also a great need for up-to-date surveys of the main lines of research designed to aid the beginner and serve as a reference for the expert. It was the aim of the Advanced Study Institute "Higher Combinatorics" in Berlin, 1976, to help fulfill this need. There were five sections: I. Counting Theory, II. Combinatorial Set Theory and Order Theory, III. Matroids, IV. Designs and V. Groups and Coding Theory, with three principal lecturers in each section. Expanded versions of most lectures form the contents of this book. The Institute was designed to offer, especially to young researchers, a comprehen­ sive picture of the most interesting developments currently under way. It is hoped that these proceedings will serve the same purpose for a wider audience.

Editors and Affiliations

  • Fachbereich Mathematik, Freie Universität Berlin, Berlin 33, Germany

    Martin Aigner

Bibliographic Information

  • Book Title: Higher Combinatorics

  • Book Subtitle: Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1–10, 1976

  • Editors: Martin Aigner

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-010-1220-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht 1977

  • Hardcover ISBN: 978-90-277-0795-6Published: 30 April 1977

  • Softcover ISBN: 978-94-010-1222-5Published: 21 December 2011

  • eBook ISBN: 978-94-010-1220-1Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: XIII, 256

  • Topics: Combinatorics

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