A recursive involution identity on the Riemann sphere generates a family of meromorphic differentials from the Bergman kernel; this establishes that all such differentials are symmetric in their arguments despite the asymmetry apparent in their recursive definition. The symmetry is proved by reducing it to a combinatorial identity for multinomial coefficients of integer partitions into a fixed number of parts. The result settles an open question in blobbed topological recursion and applies to the quartic analogue of the Kontsevich matrix model.
In topological recursion on the Riemann sphere, a family of meromorphic differentials omega^(0)_n(z_1,...,z_n) is generated recursively from the Bergman kernel and a holomorphic involution iota of P^…