# The uniqueness of plethystic factorisation

## TL;DR

This paper proves the unique factorization property of plethysm products of Schur functions and classifies certain types of these products, advancing understanding in algebraic combinatorics.

## Contribution

It establishes the first proof of unique factorization for plethysm products and classifies homogeneous and indecomposable cases.

## Key findings

- Plethysm products of Schur functions can be uniquely factorized.
- Classification of homogeneous and indecomposable plethysm products.
- Provides foundational results for algebraic combinatorics and representation theory.

## Abstract

We prove that a plethysm product of two Schur functions can be factorised uniquely and classify homogeneous and indecomposable plethysm products.