# Fast algorithm for generating ascending compositions

## TL;DR

This paper introduces a new, highly efficient algorithm for generating all ascending compositions of a positive integer, improving upon existing methods by leveraging tree structures for better performance.

## Contribution

The paper presents a novel ascending composition generation algorithm that significantly outperforms previous algorithms by utilizing tree structures for efficient enumeration.

## Key findings

- Algorithm is faster than existing methods
- Uses tree structures for efficient generation
- Applicable to systematic integer partition enumeration

## Abstract

In this paper we give a fast algorithm to generate all partitions of a positive integer $n$. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known that the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. Using tree structures for storing the partitions of integers, we develop a new ascending composition generation algorithm which is substantially more efficient than the algorithms from the literature.