Geodesic
A New Family of Bijections for Planar Maps
Séminaire lotharingien de combinatoire, 80B (2018)

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We present bijections for the planar cases of two formulas on maps that arise from the KP hierarchy (Goulden-Jackson and Carrell-Chapuy formulas), relying on a "cut-and-slide" operation. This is the first time a bijective proof is given for quadratic map-counting formulas derived from the KP hierarchy. Up to now, only the linear one-faced case was known (Harer-Zagier recurrence and Chapuy-Féray-Fusy bijection). As far as we know, this bijection is new and not equivalent to any of the well-known bijections between planar maps and tree-like objects. 

@article{SLC_2018_80B_a32,
     author = {Baptiste Louf},
     title = {A {New} {Family} of {Bijections} for {Planar} {Maps}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a32/}
}
TY  - JOUR
AU  - Baptiste Louf
TI  - A New Family of Bijections for Planar Maps
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a32/
ID  - SLC_2018_80B_a32
ER  - 
%0 Journal Article
%A Baptiste Louf
%T A New Family of Bijections for Planar Maps
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a32/
%F SLC_2018_80B_a32
Baptiste Louf. A New Family of Bijections for Planar Maps. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a32/