Many bijections between maps and decorated trees have been developed in the last 20 years, and they are often keys to the probabilistic analysis of random planar maps.
In this talk, I will present a bijection between bipartite maps and some blossoming trees, generalizing earlier work of Bousquet-Mélou and Schaeffer. As a byproduct, we derive some rational parametrization with positive integer coefficients for some maps decorated with an Ising model.
This is a joint work with Laurent Ménard and Nicolas Tokka.