Growing uniform planar maps face by face

We provide “growth schemes” for inductively generating uniform random 2 p $$ 2p -angulations of the sphere with n faces, as well simple triangulations 2n faces. In case -angulations, we a way to insert new face at location in -angulation faces such that map is precisely + 1 n+1 Similarly, given triangulation describe two adjacent triangles so obtain 2n+2 The latter based on bijective presentation relies construction by Poulalhon and Schaeffer.