A Class of lattices and boolean functions related to a Manickam-Mikl\"os-Singhi Conjecture
Cinzia Bisi, Giampiero Chiaselotti
TL;DR
This paper introduces a new family of lattices and boolean functions linked to combinatorial extremal sum problems, addressing a conjecture by Manickam, Miklós, and Singhi.
Contribution
It constructs and analyzes a novel class of lattices and boolean functions related to the Manickam-Miklós-Singhi conjecture, expanding understanding of their properties.
Findings
Established fundamental properties of the new lattices.
Defined a specific class of boolean functions on these lattices.
Provided insights into the combinatorial extremal sum problems.
Abstract
The aim of this paper is to build a new family of lattices related to some combinatorial extremal sum problems, in particular to a conjecture of Manickam, Mikl\"os and Singhi. We study the fundamentals properties of such lattices and of a particular class of boolean functions defined on them.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.