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

Abstract

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