TACTICAL DECOMPOSITIONS OF λ-SPACES

Abstract

This chapter discusses the tactical decompositions of λ-spaces. A tactical decomposition of a finite incidence structure is a decomposition of the set of its points into disjoint point classes, together with a decomposition of the set of its blocks into disjoint block classes. By a finite incidence structure, one means a set of finitely many points and finitely many blocks, together with an arbitrary incidence relation. It turns out that the class of such structures that lends itself most readily to the investigation by means of tactical decompositions is that of λ-spaces. The tactical decompositions may be successfully applied to problems different from the three stated above, for instance to the question what sub-structures certain finite incidence structures may possibly have.