# Book:Klaus Metsch/Linear Spaces with Few Lines

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## Klaus Metsch: Linear Spaces with Few Lines

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

ISBN 0-387-54720-7.

### 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