Deletions, extensions, and reductions of elliptic semiplanes

Abstract

We present three constructions which transform some symmetric configuration $\mathcal{K}$ of type $n_k$ into new symmetric configurations of types ${\left(n+1\right)}_k$, or $n_{k-1}$, or ${\left(\left(\lambda -1\right)\mu \right)}_{k-1}$ if $n=\lambda \mu$. Applying them to Desarguesian elliptic semiplanes, an infinite family of new configurations comes into being, whose types fill large gaps in the parameter spectrum of symmetric configurations.