Geodesic
Mating of discrete trees and walks in the quarter-plane
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps equipped with a rooted spanning tree and walks in the quarter plane. We also show how the construction allows to recover several known bijections between such objects in a uniform way.
DOI : 10.37236/10253
Classification : 05C05, 05C10, 05C38, 05A15
Mots-clés : planar walk, planar map, triangulation, cubic map, bijection, counting

Philippe Biane  1

1 CNRS 
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     author = {Philippe Biane},
     title = {Mating of discrete trees and walks in the quarter-plane},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/10253},
     zbl = {1473.05049},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10253/}
}
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Philippe Biane. Mating of discrete trees and walks in the quarter-plane. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10253

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