Name
Abstract | ||
|---|---|---|
We introduce a bijection between plane bipolar orientations with fixed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with some specific extremities. Writing ϑij for the number of plane bipolar orientations with (i+1) vertices and (j+1) faces, our bijection provides a combinatorial proof of the following formula due to Baxter:(1)ϑij=2(i+j−2)!(i+j−1)!(i+j)!(i−1)!i!(i+1)!(j−1)!j!(j+1)!. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.endm.2007.07.049 | Electronic Notes in Discrete Mathematics |
Keywords | Field | DocType |
bijection,bipolar orientations,non-intersecting paths | Discrete mathematics,Combinatorics,Bijection,Vertex (geometry),Lattice (order),Combinatorial proof,Mathematics | Journal |
Volume | ISSN | Citations |
29 | 1571-0653 | 2 |
PageRank | References | Authors |
0.38 | 11 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Éric Fusy | 1 | 198 | 21.95 |
| Dominique Poulalhon | 2 | 127 | 9.73 |
| Gilles Schaeffer | 3 | 423 | 44.82 |