Geodesic
A simple formula for the series of constellations and quasi-constellations with boundaries
Gwendal Collet1 ; Éric Fusy1
1LIX, Ecole Polytechnique 91220 Palaiseau cedex, France
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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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).
DOI : 10.37236/3472
Classification : 05C10, 05C30
Mots-clés : planar maps, bijections

Gwendal Collet  1   ; Éric Fusy  1

1 LIX, Ecole Polytechnique 91220 Palaiseau cedex, France 
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Gwendal Collet; Éric Fusy. A simple formula for the series of constellations and quasi-constellations with boundaries. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3472

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