Bijective counting of plane bipolar orientations and Schnyder woods
| dc.creator | Fusy, Eric | |
| dc.creator | Poulalhon, Dominique | |
| dc.creator | Schaeffer, Gilles | |
| dc.date | 2008-03-04 | |
| dc.date | 2009-03-20 | |
| dc.date.accessioned | 2026-07-07T12:54:00Z | |
| dc.date.available | 2026-07-07T12:54:00Z | |
| dc.description | A bijection $Φ$ is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities. This yields a combinatorial proof of the following formula due to R. Baxter for the number $Θ_{ij}$ of plane bipolar orientations with $i$ non-polar vertices and $j$ inner faces: $Θ_{ij}=2\frac{(i+j)!(i+j+1)!(i+j+2)!}{i!(i+1)!(i+2)!j!(j+1)!(j+2)!}$. In addition, it is shown that $Φ$ specializes into the bijection of Bernardi and Bonichon between Schnyder woods and non-crossing pairs of Dyck words. | |
| dc.description | An extended abstract describing the bijection without proofs has appeared in the proceedings of Eurocomb'07 | |
| dc.identifier | https://arxiv.org/abs/0803.0400 | |
| dc.identifier | http://arxiv.org/abs/0803.0400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223783 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | Bijective counting of plane bipolar orientations and Schnyder woods | |
| dc.type | text |