On the Frankl's union-closed conjecture
Abstract
A celebrated unresolved conjecture of Peter Frankl states that every finite collection of sets, with finite universe, admits an abundant element. In this paper, we prove Frankl's union-closed conjecture(FC). We provide an induction proof based on a key result that every candidate collection, , admits an irreducible form. The concept of irreducible collections is one of the key contributions of this paper. We show that the conjecture is true if it holds for a class of irreducible finite collections. Then we show that the conjecture holds for all irreducible finite collections, with non-empty universe.
Keywords
Cite
@article{arxiv.1805.09695,
title = {On the Frankl's union-closed conjecture},
author = {Acquaah Peter},
journal= {arXiv preprint arXiv:1805.09695},
year = {2019}
}
Comments
This document is work in progress. Its current form is wrong! Some readers pointed out how to correct the paper.Therefore, the serious typo and error can be corrected. Therefore, the paper will be modified seriously and submitted