%0 Journal Article
%T A simple formula for the series of constellations and quasi-constellations with boundaries
%A Gwendal Collet
%A Eric Fusy
%J Mathematics
%D 2012
%I arXiv
%X We obtain a very simple formula for the generating function of bipartite (resp. quasi-bipartite) planar maps with boundaries (holes) of prescribed lengths, which generalizes certain expressions obtained by Eynard in a book to appear. The formula is derived from a bijection due to Bouttier, Di Francesco and Guitter combined with a process (reminiscent of a construction of Pitman) of aggregating connected components of a forest into a single tree. The formula naturally extends to $p$-constellations and quasi-$p$-constellations with boundaries (the case $p=2$ corresponding to bipartite maps).
%U http://arxiv.org/abs/1205.5215v3