Geodesic
Parking Functions and Labeled Trees
Séminaire lotharingien de combinatoire, Tome 65 (2011-2012)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We define a bijection between the set of parking functions of size n and the set of rooted (labeled) forests with n vertices for which the number of "probes" of the function is the number of inversions of the tree. This definition is not recursive. 

@article{SLC_2011-2012_65_a4,
     author = {Ant\'onio Guedes de Oliveira and Michel Las Vergnas},
     title = {Parking {Functions} and {Labeled} {Trees}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {65},
     year = {2011-2012},
     url = {http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a4/}
}
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António Guedes de Oliveira; Michel Las Vergnas. Parking Functions and Labeled Trees. Séminaire lotharingien de combinatoire, Tome 65 (2011-2012). http://geodesic.mathdoc.fr/item/SLC_2011-2012_65_a4/