Book:Klaus Metsch/Linear Spaces with Few Lines

Klaus Metsch: Linear Spaces with Few Lines

Published $\text {1991}$, Springer-Verlag

ISBN 0-387-54720-7

Subject Matter

• Projective Geometry

Contents

Introduction

1. Definitions and basic properties of linear spaces

2. Lower bounds for the number of lines

3. Basic properties and results on $(n+1,1)$-designs

4. Points of degree $n$

5. Linear spaces with few lines

6. Embedding $(n+1,1)$-designs in projective planes

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

8. The Theorem of Totten

9. Linear spaces with $n^2+n+1$ points

10. A hypothetical structure

11. Linear spaces with $n^2+n+2$ lines

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

13. The non-Existence of certain $(7, 1)$-designs and determination of $A(5)$ and $A(6)$

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

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

16. $s$-fold inflated projective planes

17. The Dowling-Wilson Conjecture

18. Uniqueness of embeddings

References

Index