Slit-slide-sew bijections for bipartite and quasibipartite plane maps - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Seminaire Lotharingien de Combinatoire Année : 2019

Slit-slide-sew bijections for bipartite and quasibipartite plane maps

Résumé

We unify and extend previous bijections on plane quadrangulations to bi-partite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different faces), we build a new plane map with a distinguished vertex and two distinguished half-edges directed toward the vertex. The faces of the new map have the same degree as those of the original map, except at the locations of the distinguished corners, where each receives an extra degree. The idea behind this bijection is to build a path from the distinguished elements, slit the map along it, and sew back after sliding by one unit, thus mildly modifying the structure of the map at the extremities of the sliding path. This bijection allows to recover Tutte's famous counting formula for bipartite and quasibipartite plane maps. In addition, we explain how to decompose the previous bijection into two more elementary ones, which each transfer a degree from one face of the map to another face. In particular, these transfer bijections are simpler to manipulate than the previous one and this point of view simplifies the proofs.
Fichier principal
Vignette du fichier
XX_sss_quasibip_short.pdf (773.8 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02347579 , version 1 (05-11-2019)

Identifiants

  • HAL Id : hal-02347579 , version 1

Citer

Jérémie Bettinelli. Slit-slide-sew bijections for bipartite and quasibipartite plane maps. Seminaire Lotharingien de Combinatoire, In press, 82B (Art. 82), pp.1--12. ⟨hal-02347579⟩
20 Consultations
47 Téléchargements

Partager

Gmail Facebook X LinkedIn More