Linear Spaces with Few Lines

  • Authors
  • Klaus┬áMetsch

Part of the Lecture Notes in Mathematics book series (LNM, volume 1490)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Klaus Metsch
    Pages 9-14
  3. Klaus Metsch
    Pages 21-30
  4. Klaus Metsch
    Pages 31-42
  5. Klaus Metsch
    Pages 74-85
  6. Klaus Metsch
    Pages 86-93
  7. Klaus Metsch
    Pages 94-105
  8. Klaus Metsch
    Pages 106-117
  9. Klaus Metsch
    Pages 161-180
  10. Klaus Metsch
    Pages 181-187
  11. Klaus Metsch
    Pages 188-191
  12. Back Matter
    Pages 192-196

About this book

Introduction

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.

Keywords

Combinatorics Embeddings Finite Linear Space boundary element method character design eXist field graph graph theory proof techniques theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0083245
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54720-4
  • Online ISBN 978-3-540-46444-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book