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Bijective counting of plane bipolar orientations and Schnyder woods
- Source :
-
European Journal of Combinatorics . Oct2009, Vol. 30 Issue 7, p1646-1658. 13p. - Publication Year :
- 2009
-
Abstract
- Abstract: A bijection 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 Baxter for the number of plane bipolar orientations with non-polar vertices and inner faces: In addition, it is shown that specializes into the bijection of Bernardi and Bonichon between Schnyder woods and non-crossing pairs of Dyck words. This is the extended and revised journal version of a conference paper with the title “Bijective counting of plane bipolar orientations”, which appeared in Electr. Notes in Discr. Math. pp. 283–287 (Proceedings of Eurocomb’07, 11–15 September 2007, Sevilla). [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 30
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 43319564
- Full Text :
- https://doi.org/10.1016/j.ejc.2009.03.001