Finite linear spaces in which any n-gon is euclidean
✍ Scribed by Albrecht Beutelspacher; Inge Schestag
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 896 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
An n-gon of a linear space is a set S of n points no three of which are coUinear. By a diagonal point of S we mean a point p off S with the property that at least two lines through p intersect S in two points. The number of diagonal points is called the type of S. For example, a 4-gon has at most three diagonal points. We call an n-gon euclidean if (roughly speaking) it contains the maximal possible number of 4-gons of type 3. In this paper, we characterize all finite linear spaces in which, for a fixed number n ~> 5, any n-gon is euclidean.
It turns out that these structures are essentially projective spaces or punctured projective spaces.