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

Abstract

We prove that meromorphic differentials ${\omega }_n^{(0)}(z_1,...,z_n)$ 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.

29 pages. Conjecture 1 of v1 is Theorem 1 in v2 with proof in sec. 6