  In this work, we expose four bijections each allowing to increase (or
decrease) one parameter in either uniform random forests with a fixed number of
edges and trees, or quadrangulations with a boundary having a fixed number of
faces and a fixed boundary length. In particular, this gives a way to sample a
uniform quadrangulation with n + 1 faces from a uniform quadrangulation with n
faces or a uniform forest with n+1 edges and p trees from a uniform forest with
n edges and p trees.
