Shadows in Linear Lattices

Abstract

this paper we investigate the Kruskal-Katona type problem for linear lattices. First (section 2) we show that there is a dual problem to the minimization problem, namely the maximization of the cardinality of the "reverse shadow" which will be defined later. We prove that the minimization problem and the maximization problem are equisolvable. In section 3 we relax the problem by asking for which subset S of (GF (q)