Skip to Main content Skip to Navigation
Conference papers

New bijective links on planar maps

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.
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185163
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, August 19, 2015 - 11:43:03 AM
Last modification on : Friday, December 18, 2020 - 5:12:01 PM
Long-term archiving on: : Friday, November 20, 2015 - 10:33:43 AM

File

dmAJ0114.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185163, version 1

Collections

Citation

Eric Fusy. New bijective links on planar maps. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.153-166. ⟨hal-01185163⟩

Share

Metrics

Record views

155

Files downloads

610