Name
Abstract | ||
|---|---|---|
Unicellular maps are a natural generalisation of plane trees to higher genus surfaces. In this article we study covered maps, which are maps together with a distinguished unicellular spanning submap. We prove that the covered maps of genus g with n edges are in bijection with pairs made of a plane tree with n edges and a bipartite unicellular map of genus g with n+1 edges. This generalises to any genus the bijection given in [O. Bernardi. Bijective counting of tree-rooted maps and shuffles of parenthesis systems. Electron. J. Combin., 14(1): Research Paper 9, 36 pp., 2007] between planar tree-rooted maps (maps with a distinguished spanning tree) and pairs made of a tree with n edges and a tree with n+1 edges. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.endm.2008.06.010 | Electronic Notes in Discrete Mathematics |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Bijection,Generalization,Bipartite graph,Spanning tree,Parenthesis,Mathematics | Journal | 31 |
ISSN | Citations | PageRank |
1571-0653 | 0 | 0.34 |
References | Authors | |
3 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olivier Bernardi | 1 | 106 | 14.20 |
| Guillaume Chapuy | 2 | 73 | 11.25 |