A note on transitive union-closed families

TL;DR

This paper proves that the Union-Closed Conjecture is valid for a specific class of union-closed families generated by cyclic translations of a fixed set, advancing understanding of the conjecture.

Contribution

It establishes the validity of the Union-Closed Conjecture for families generated by cyclic translates, a new class not previously confirmed.

Findings

Union-Closed Conjecture holds for cyclic translate-generated families

Provides a proof for a specific class of union-closed families

Advances the theoretical understanding of the conjecture

Abstract

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.