New bijective links on planar maps via orientations

dc.creatorFusy, Eric
dc.date2008-10-15
dc.date2009-03-20
dc.date.accessioned2026-07-07T12:54:08Z
dc.date.available2026-07-07T12:54:08Z
dc.descriptionThis article presents new bijections on planar maps. At first a bijection is established between bipolar orientations on planar maps and specific "transversal structures" on triangulations of the 4-gon with no separating 3-cycle, which are called irreducible triangulations. This bijection specializes to a bijection between rooted non-separable maps and rooted irreducible triangulations. This yields in turn a bijection between rooted loopless maps and rooted triangulations, based on the observation that loopless maps and triangulations are decomposed in a similar way into components that are respectively non-separable maps and irreducible triangulations. This gives another bijective proof (after Wormald's construction published in 1980) of the fact that rooted loopless maps with $n$ edges are equinumerous to rooted triangulations with $n$ inner vertices.
dc.descriptionExtended and revised journal version of a conference paper with the title "New bijective links on planar maps", which appeared in the Proceedings of FPSAC'08, 23-27 June 2008, Viña del Mar
dc.identifierhttps://arxiv.org/abs/0810.2607
dc.identifierhttp://arxiv.org/abs/0810.2607
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223825
dc.subjectCombinatorics
dc.subject05A15
dc.titleNew bijective links on planar maps via orientations
dc.typetext

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