ABSTRACT
There is a more or less classical geometry called a Sperner space, the theory of which essentially parallels the theory of translation planes. We have discussed spreads for translation planes. In this setting, we have a 2n dimension vector space over GF (q) and a set of mutually disjoint (as subspaces) n-dimensional subspaces forming a partition of the non-zero vectors. If we relax the condition that the partition of subspaces be n-dimensional, and define the resulting geometry by taking points as vectors and lines as translates of the ‘spread’ subspaces, we would obtain a Sperner space.
