A bijection between planar constellations and some colored Lagrangian trees - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2003

A bijection between planar constellations and some colored Lagrangian trees

Résumé

Constellations are colored planar maps that generalize different families of maps (planar maps, bipartite planar maps, bi-Eulerian planar maps, planar cacti, ...) and are strongly related to factorizations of permutations. They were recently studied by Bousquet-Mélou and Schaeffer who describe a correspondence between these maps and a family of trees, called Eulerian trees. In this paper, we derive from their result a relationship between planar constellations and another family of trees, called stellar trees. This correspondence generalizes a well known result for planar cacti, and shows that planar constellations are colored Lagrangian objects (that is objects that can be enumerated by the Good-Lagrange formula). We then deduce from this result a new formula for the number of planar constellations having a given face distribution, different from the formula one can derive from the results of Bousquet-Mélou and Schaeffer, along with systems of functional equations for the generating functions of bipartite and bi-Eulerian planar maps enumerated according to the partition of faces and vertices.
Fichier principal
Vignette du fichier
dm060102.pdf (202.04 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00958985 , version 1 (13-03-2014)

Identifiants

Citer

Cedric Chauve. A bijection between planar constellations and some colored Lagrangian trees. Discrete Mathematics and Theoretical Computer Science, 2003, Vol. 6 no. 1 (1), pp.13-40. ⟨10.46298/dmtcs.340⟩. ⟨hal-00958985⟩

Collections

TDS-MACS
42 Consultations
833 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More