On the lattice formulation of the union-closed sets conjecture
Keywords:
union-closed sets conjecture, Frankl's conjecture, latticeAbstract
The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice L with more than one element contains a join-irreducible element that is less than or equal to at most half of the elements in L. In this work, we obtain several necessary conditions for any counterexample L of minimum size.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Christopher Bouchard
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
