Gwendal Collet ; Eric Fusy
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A simple formula for bipartite and quasi-bipartite maps with boundaries
dmtcs:3067 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2012,
DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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https://doi.org/10.46298/dmtcs.3067
A simple formula for bipartite and quasi-bipartite maps with boundaries
Authors: Gwendal Collet 1; Eric Fusy 1
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Gwendal Collet;Eric Fusy
1 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.
Combinatorial methods, from enumerative topology to random discrete structures and compact data representations.; Funder: European Commission; Code: 208471