On Linear Representations of (α, β)-Geometries

In [11] P. J. Cameron introduced partial quadrangles and raised the question of finding a characterization of partial quadrangles which have linear representations. An almost complete answer was given in [9]: the proof was a number-theoretic one. In this paper we discuss the question for a more general class of geometries, namely the (α, β)-geometries. We shall specialize to the case of (0,1)-geometries, and we shall give a geometric characterization of the partial quadrangle T*2 (O).