A simple formula for the series of constellations and quasi-constellations with boundaries

Gwendal Collet (1) , Eric Fusy (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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).

Domaines: Combinatoire [math.CO]

Gwendal Collet, Eric Fusy. A simple formula for the series of constellations and quasi-constellations with boundaries. The Electronic Journal of Combinatorics, 2014, 21 (2), pp.P2.9. ⟨hal-01188343⟩