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Linear Spaces with Few Lines

  • Book
  • © 1991

Overview

Authors:
  1. Klaus Metsch
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1490)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XII
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  2. Definition and basic properties of linear spaces

    • Klaus Metsch
    Pages 1-8

  3. Lower bounds for the number of lines

    • Klaus Metsch
    Pages 9-14

  4. Basic properties and results of (n+1,1)-designs

    • Klaus Metsch
    Pages 15-20

  5. Points of degree n

    • Klaus Metsch
    Pages 21-30

  6. Linear spaces with few lines

    • Klaus Metsch
    Pages 31-42

  7. Embedding (n+1,1)-designs into projective planes

    • Klaus Metsch
    Pages 43-60

  8. An optimal bound for embedding linear spaces into projective planes

    • Klaus Metsch
    Pages 61-73

  9. The theorem of totten

    • Klaus Metsch
    Pages 74-85

  10. Linear spaces with n2+n+1 points

    • Klaus Metsch
    Pages 86-93

  11. A hypothetical structure

    • Klaus Metsch
    Pages 94-105

  12. Linear spaces with n2+n+2 lines

    • Klaus Metsch
    Pages 106-117

  13. Points of degree n and another characterization of the linear spaces L(n,d)

    • Klaus Metsch
    Pages 118-130

  14. The non-existence of certain (7,1)-designs and determination of A(5) and A(6)

    • Klaus Metsch
    Pages 131-140

  15. A result on graph theory with an application to linear spaces

    • Klaus Metsch
    Pages 141-149

  16. Linear spaces in which every long line meets only few lines

    • Klaus Metsch
    Pages 150-160

  17. s-fold inflated projective planes

    • Klaus Metsch
    Pages 161-180

  18. The Dowling Wilson Conjecture

    • Klaus Metsch
    Pages 181-187

  19. Uniqueness of embeddings

    • Klaus Metsch
    Pages 188-191

  20. Back Matter

    Pages 192-196
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Keywords

About this book

A famous theorem in the theory of linear spaces states that every finite linear space has at least as many lines as points. This result of De Bruijn and Erd|s led to the conjecture that every linear space with "few lines" canbe obtained from a projective plane by changing only a small part of itsstructure. Many results related to this conjecture have been proved in the last twenty years. This monograph surveys the subject and presents several new results, such as the recent proof of the Dowling-Wilsonconjecture. Typical methods used in combinatorics are developed so that the text can be understood without too much background. Thus the book will be of interest to anybody doing combinatorics and can also help other readers to learn the techniques used in this particular field.

Bibliographic Information

  • Book Title: Linear Spaces with Few Lines

  • Authors: Klaus Metsch

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0083245

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54720-4Published: 23 October 1991

  • eBook ISBN: 978-3-540-46444-0Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 202

  • Topics: Combinatorics

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