Entropy approach for a generalization of Frankl's conjecture

TL;DR

This paper employs an entropy-based method to establish a comprehensive condition for identifying elements that are present in at least half of the sets within a finite family, advancing understanding of Frankl's conjecture.

Contribution

It introduces an entropy approach that generalizes Frankl's conjecture by providing a necessary and sufficient condition for element membership in at least half of the sets.

Findings

Derived a necessary and sufficient condition using entropy methods.

Extended the understanding of Frankl's conjecture.

Provided a new analytical framework for set family analysis.

Abstract

In this paper, we will use the entropy approach to derive a necessary and sufficient condition for the existence of an element that belongs to at least half of the sets in a finite family of sets.