New bijective links on planar maps via orientations
| dc.creator | Fusy, Eric | |
| dc.date | 2008-10-15 | |
| dc.date | 2009-03-20 | |
| dc.date.accessioned | 2026-07-07T12:54:08Z | |
| dc.date.available | 2026-07-07T12:54:08Z | |
| dc.description | This 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.description | Extended 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.identifier | https://arxiv.org/abs/0810.2607 | |
| dc.identifier | http://arxiv.org/abs/0810.2607 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223825 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | New bijective links on planar maps via orientations | |
| dc.type | text |