$k$-sets of type $(1, h)$ in finite planar spaces

Abstract

A set of type $(m,n)$ is a set  $\mathcal K$ of points of a planarspace with the  property that each plane of the space meets$\mathcal K$ either in $m$ or $n$ points, and there are both planesintersecting $\mathcal K$ in $m$ points and in $n$ points. Inthis paper, sets of type $(1, h)$ in a planar space whose planespairwise intersect either in the empty--set or in a line, are studied.