  We obtain simple quadratic recurrence formulas counting bipartite maps on
surfaces with prescribed degrees (in particular, $2k$-angulations), and
constellations. These formulas are the fastest known way of computing these
numbers. Our work is a natural extension of previous works on integrable
hierarchies (2-Toda and KP), namely the Pandharipande recursion for Hurwitz
numbers (proven by Okounkov and simplified by Dubrovin-Yang-Zagier), as well as
formulas for several models of maps (Goulden-Jackson, Carrell-Chapuy,
Kazarian-Zograf). As for those formulas, a bijective interpretation is still to
be found. We also include a formula for monotone simple Hurwitz numbers derived
in the same fashion. These formulas also play a key role in subsequent work of
the author with T. Budzinski establishing the hyperbolic local limit of random
bipartite maps of large genus.
