# Book:Klaus Metsch/Linear Spaces with Few Lines

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## Klaus Metsch:

## Klaus Metsch: *Linear Spaces with Few Lines*

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

- ISBN 0-387-54720-7.

### Subject Matter

### 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