Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions

TL;DR

This paper proves that certain meromorphic differentials generated by an involution identity are symmetric in all variables, using a combinatorial identity related to integer partitions.

Contribution

It establishes the symmetry of meromorphic differentials produced by involution identities and links this property to a combinatorial identity involving integer partitions.

Findings

Meromorphic differentials are symmetric in all arguments.

A combinatorial identity between integer partitions is key to the proof.

The symmetry property is proven for differentials generated recursively by involution.

Abstract

We prove that meromorphic differentials $\omega^{(0)}_n(z_1,...,z_n)$ which are recursively generated by an involution identity are symmetric in all their arguments $z_1,...,z_n$. The proof involves an intriguing combinatorial identity between integer partitions into given number of parts.