Optimal shadows and ideals in submatrix orders

U Leck - Discrete mathematics, 2001 - Elsevier
U Leck
Discrete mathematics, 2001Elsevier
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.
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.
Elsevier
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