# A Note on the Frankl Conjecture

## TL;DR

This paper explores variants of the Frankl conjecture, a well-known unsolved problem in combinatorics, by introducing and partially justifying new conjectural forms.

## Contribution

It proposes and provides initial justification for several variants of the Frankl conjecture, expanding the scope of potential approaches.

## Key findings

- Introduction of new variants of the Frankl conjecture
- Partial theoretical justification for these variants
- Potential implications for future research in combinatorics

## Abstract

The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.