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Lecture Notes in Mathematics

Linear Spaces with Few Lines

Authors: Metsch, Klaus

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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.

Table of contents (18 chapters)

Table of contents (18 chapters)
  • Definition and basic properties of linear spaces

    Pages 1-8

    Metsch, Klaus

  • Lower bounds for the number of lines

    Pages 9-14

    Metsch, Klaus

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

    Pages 15-20

    Metsch, Klaus

  • Points of degree n

    Pages 21-30

    Metsch, Klaus

  • Linear spaces with few lines

    Pages 31-42

    Metsch, Klaus

Buy this book

eBook $24.99
price for USA in USD
  • ISBN 978-3-540-46444-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $33.00
price for USA in USD
  • ISBN 978-3-540-54720-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Linear Spaces with Few Lines
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1490
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46444-0
DOI
10.1007/BFb0083245
Softcover ISBN
978-3-540-54720-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 202
Topics

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