# Integral factorial ratios: Irreducible examples with height larger than 1

## TL;DR

This paper classifies and constructs numerous irreducible integral factorial ratios with height 2, expanding understanding of their structure and providing over 50 two-parameter families with specific properties.

## Contribution

It offers a classification of integral factorial ratios with height 2, including a general construction of more than 50 two-parameter families, and proves their irreducibility.

## Key findings

- Classified factorial ratios with height 2 and norm ≤ 1/3
- Constructed over 50 two-parameter families of such ratios
- Proved these ratios are irreducible, not derived from height 1 ratios

## Abstract

This paper discusses examples of integral factorial ratios of height 2 or more. It classifies (apart from finitely many examples) such factorial ratios with height 2 and norm at most 1/3, and describes a general result which exhibits more than 50 two parameter families of integral factorial ratios with height 2. These examples are shown to be irreducible in the sense that they do not arise from multiplying two factorial ratios of height 1.