Book:Klaus Metsch/Linear Spaces with Few Lines

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