The nonexistence of ovals in a projective plane of order 10
β Scribed by C.W.H. Lam; L. Thiel; S. Swiercz; J. McKay
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 325 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
This paper reports the result of a computer search which show s that there is no oval in a projective plane of order 10. It gives a brief description of the search method as well as a brief survey of other possible configurations in a plane of order 10.
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.
A configuration D with parameters (u, b, r. k) is an incidence structure t P, B. 2 L where ? is a set of u "points'\*, 8 is a set of b '"blocks" and 7 is an 'incidence relation" between points and blocks such that each point is incident with t blocks, and each blok is incident with Fc points. A bloc
## Abstract In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}\_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. A