Computer Visualization in Search for Geometric (n_k) Configurations and Incidence Theorems
Presented by Dr. Gábor GéVAY
Type: Oral presentation
In the simplest case, a geometric $(n_k)$ configuration is a set of $n$ points and $n$ lines such that each of the points is incident with precisely $k$ of the lines and each of the lines is incident with precisely $k$ of the points. Instead of lines, the second subset can consist of planes, hyperplanes, circles, ellipses, etc. We present some new classes of highly symmetric spatial point-line configurations, and of planar point-circle configurations. In constructing these configurations computer visualization played an important heuristic role. The same is valid for certain new incidence statements which we also briefly discuss. These results have been obtained partly in joint work with Toma\v z Pisanski.