Abstract:
We consider generating series of hypermaps with controlled degrees of vertices, hyperedges and faces. It is well known that under some particular specializations, these series satisfy the celebrated KP equations in the orientable case, and BKP equations in the non-orientable one. In this talk, I present a family of differential equations which characterizes the full generating series of hypermaps.
I will give a first proof which works for a one parameter deformation of the series of hypermaps related to Jack polynomials. This proof is based on a differential formula for Jack characters obtained in a joint work with Maciej Dołęga. I will also present a combinatorial proof for the orientable case.
