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