Bicolored maps with boundaries can be seen as a special, simple case of the Ising model on maps. However, they are yet to be enumerated explicitly. I will present in this talk a work in progress in collaboration with Jérémie Bouttier, where we used analytic-combinatorial tools for the specific case of planar bicolored maps with alternating boundaries. This yields an explicit rational parametrization in the case of m-angulations and m-constellations. In the special case of Eulerian triangulations, this rational parametrization was a key ingredient in proving in https://arxiv.org/abs/1912.13434 that this family of maps admits the Brownian map as a scaling limit.
Joseph Ben Geloun
Fabien Vignes-Tourneret
