Geodesic
Bijective Proof of the Rationality of the Generating Series of Higher-Genus Maps
Séminaire lotharingien de combinatoire, 80B (2018)

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Bender and Canfield proved in 1991 that the generating series of maps in higher genus is a rational function of the generating series of planar maps. In this paper, we give the first bijective proof of this result. Our approach starts with the introduction of a canonical orientation that enables us to construct a bijection between $4$-valent bicolorable maps and a family of unicellular blossoming maps. 

@article{SLC_2018_80B_a66,
     author = {Mathias Lepoutre},
     title = {Bijective {Proof} of the {Rationality} of the {Generating} {Series} of {Higher-Genus} {Maps}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a66/}
}
TY  - JOUR
AU  - Mathias Lepoutre
TI  - Bijective Proof of the Rationality of the Generating Series of Higher-Genus Maps
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a66/
ID  - SLC_2018_80B_a66
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%0 Journal Article
%A Mathias Lepoutre
%T Bijective Proof of the Rationality of the Generating Series of Higher-Genus Maps
%J Séminaire lotharingien de combinatoire
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%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a66/
%F SLC_2018_80B_a66
Mathias Lepoutre. Bijective Proof of the Rationality of the Generating Series of Higher-Genus Maps. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a66/