In this talk we will see how the discrete Painlevé I and II equations appear in two different and well-known combinatorial problems : the first one in relation with planar maps and the second one instead in the study of the Poissonized Plancherel measure for random partitions. We will see that the common denominator behind these phenomenon is the presence of orthogonal polynomials. We will further explain how this tool allows us to extend these results from one side for the two-point functions for planar maps and from the other side for multicritical Schur measures for random partitions (based on work in progress with J. Bouttier and a collaboration with T. Chouteau).
