Abstract :
The main result of this article is in proving a conjecture by Sali. We obtain a Kruskal–Katona-type theorem for the poset P(N;A,B), which for a finite set N and disjoint subsets A,B⊆N is the set {F⊆N | F∩A≠∅≠F∩B}, ordered by inclusion. Such posets are known as submatrix orders. As an application we give a solution to the problem of finding an ideal of given size and maximum weight in submatrix orders and in their duals.
