6533b831fe1ef96bd1299a4a
RESEARCH PRODUCT
Finite linear spaces in which any n-gon is euclidean
I SchestagAlbrecht Beutelspachersubject
Discrete mathematicsLinear spaceDiagonalComputer Science::Computational GeometryEuclidean distance matrixTheoretical Computer ScienceCombinatoricsEuclidean geometryHomographyAffine spaceMathematics::Metric GeometryDiscrete Mathematics and CombinatoricsPoint (geometry)Linear separabilityMathematicsdescription
Abstract An n-gon of a linear space is a set S of n points no three of which are collinear. 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1986-05-01 | Discrete Mathematics |