Increasing Forests and Quadrangulations via a Bijective Approach
  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. 
J\'er\'emie Bettinelli (IECL)
math.PR cs.DM math.CO