Some Results on Odd Astral Configurations

Abstract

An astral configuration $(p_q, n_k)$ is a collection of $p$ points and $n$ straight lines in the Euclidean plane where every point has $q$ straight lines passing through it and every line has $k$ points lying on it, with precisely $\lfloor {q+1\over 2} \rfloor$ symmetry classes (transitivity classes) of lines and $\lfloor {k+1\over 2} \rfloor$ symmetry classes of points. An odd astral configuration is an astral configuration where at least one of $q$ and $k$ is odd. This paper presents all known results in the classification of odd astral configurations where $q$ and $k$ are both at least 4.