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Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2004

Planar maps as labeled mobiles

Résumé

We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences, to obtain a bijection with a new class of labeled trees, which we call mobiles. Our bijection covers all the classes of maps previously enumerated by either the two-matrix model used by physicists or by the bijection with blossom trees used by combinatorists. Our bijection reduces the enumeration of maps to that, much simpler, of mobiles and moreover keeps track of the geodesic distance within the initial maps via the mobiles' labels. Generating functions for mobiles are shown to obey systems of algebraic recursion relations.

Dates et versions

hal-00586658 , version 1 (18-04-2011)

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Jérémie Bouttier, Philippe Di Francesco, Emmanuel Guitter. Planar maps as labeled mobiles. The Electronic Journal of Combinatorics, 2004, 11, pp.R69. ⟨hal-00586658⟩
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