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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.