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- W68716244 abstract "This article describes new bijective links on planar maps, which are of incremental complexity and present original features. The first two bijections $Phi _{1,2}$ are correspondences on oriented planar maps. They can be considered as variations on the classical edge-poset construction for bipolar orientations on graphs, suitably adapted so as to operate only on the embeddings in a simple local way. In turn, $Phi_{1,2}$ yield two new bijections $F_{1,2}$ between families of (rooted) maps. (i) By identifying maps with specific constrained orientations, $Phi_2 circ Phi_1$ specialises to a bijection $F_1$ between 2-connected maps and irreducible triangulations; (ii) $F_1$ gives rise to a bijection $F_2$ between loopless maps and triangulations, observing that these decompose respectively into 2-connected maps and into irreducible triangulations in a parallel way. Cet article décrit de nouveaux liens bijectifs sur les cartes planaires. Nos constructions sont de complexité croissante et présentent des caractéristiques originales. Les deux premières bijections $Phi _{1,2}$ portent sur des cartes orientées. Elle peuvent être vues comme des variations sur une construction classique de posets sans $N$ à partir d'orientations bipolaires, adaptées ici pour opérer de manière très simple sur le plongement. Les bijections $Phi _{1,2}$ entrainent à leur tour deux nouvelles bijections $F_{1,2}$ entre familles de cartes (enracinées). (i) En identifiant les cartes avec certaines orientations contraintes, $Phi_2 circ Phi_1$ se spécialise en une bijection $F_1$ entre cartes 2-connexes et triangulations irréductibles, (ii) $F_1$ induit une bijection $F_2$ entre cartes sans boucles et triangulations, qui se décomposent respectivement en cartes 2-connexes et en triangulations irréductibles de manière parallèle." @default.
- W68716244 created "2016-06-24" @default.
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- W68716244 date "2008-01-01" @default.
- W68716244 modified "2023-09-26" @default.
- W68716244 title "New bijective links on planar maps" @default.
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- W68716244 doi "https://doi.org/10.46298/dmtcs.3628" @default.
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