Pseudo-Complements in Finite Projective Planes

Abstract

We show that a finite linear space with $b=n^2+n+1$ lines, $n\ge 2$, constant point-degree $n+1$ and containing a sufficient number of lines of size $n$ can be embedded in a projective plane of order $n$. Using this fact, we also give characterizations of some pseudo-complements, which are the complements of certain subsets of finite projective planes.