A \((0, 1)\) — Matrix Framework for Elliptic Semiplanes

Abstract

We present algebraic constructions yielding incidence matrices for all finite Desarguesian elliptic semiplanes of types \(C, D\), and \(L\). Both basic ingredients and suitable notations are derived from addition and multiplication tables of finite fields. This approach applies also to the only elliptic semiplane of type B known so far. In particular, the constructions provide intrinsic tactical decompositions and partitions for these elliptic semiplanes into elliptic semiplanes of smaller order.