It is shown that in every n-coiouring ((n -1)-colouring) of a projective plane (affme plane) of odd order n at least one line has three points of the same colour. Using clever counting arguments, Kabell proves that "In any n-coloring of PG(2, n), at least one line contains points of at most n-1 co
Orthogonal polarities of finite projective planes of odd order
β Scribed by Manfred Seib
- Publisher
- Springer
- Year
- 1973
- Tongue
- English
- Weight
- 108 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
β¦ Synopsis
ORTHOGONAL POLARITIES OF FINITE PROJECTIVE PLANES OF ODD ORDER
ORTHOGONAL POLARITIES (I0) A is transitive on the points of P.
From ( ) and ( ) it now follows that P is desarguesian [3].
π SIMILAR VOLUMES
Let be a projective plane of odd order n containing an oval β. We give a classification of collineation groups of which fix β and act transitively on the set I I of all internal points of β.
Lam, C.W.H., G. Kolesova and L. Thiel, A computer search for iinite projective planes of order 9, Discrete Mathematics 92 (1991) 187-195. There are four known finite projective planes of order 9. This paper reports the result of a computer search which shows that this list is complete. The computer