Classical mixed partitions

Abstract

Through a method given in Hirschfeld and Thas (General Galois Geometries, Oxford University Press, Oxford, 1991), a mixed partition of PG(2 n −1, q 2 ) can be used to construct a (2 n −1)-spread of PG(4 n −1, q ) and, hence, a translation plane of order q 2 n . A mixed partition in this case is a partition of the points of PG(2 n −1, q 2 ) into PG( n −1, q 2 )'s and PG(2 n −1, q )'s which we call Baer subspaces. In this paper, we completely classify the mixed partitions which generate regular spreads and, hence, can be classified as classical .