# Generation of Union Closed Sets and Moore families

## TL;DR

This paper presents an algorithm for enumerating non-isomorphic Union closed Sets and Moore families, confirming known counts for small sets and providing new counts for larger sets, highlighting computational challenges for larger sizes.

## Contribution

The authors develop a constructive enumeration algorithm for Union closed Sets and Moore families, confirming existing counts and extending to n=7 elements, revealing growth challenges.

## Key findings

- Confirmed counts for n<=6 elements
- Provided counts for n=7 elements
- Highlighting computational complexity for n>=8

## Abstract

In this article we will describe an algorithm to constructively enumerate non-isomorphic Union closed Sets and Moore sets. We confirm the number of isomorphism classes of Union closed Sets and Moore sets on n<=6 elements presented by other authors and give the number of isomorphism classes of Union closed Sets and Moore sets on 7 elements. Due to the enormous growth of the number of isomorphism classes it seems unlikely that constructive enumeration for 8 or more elements will be possible in the foreseeable future.