Geodesic
A combinatorial identity concerning plane colored trees and its applications
Journal of integer sequences, Tome 20 (2017) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this note, we obtain a combinatorial identity by counting some colored plane trees. This identity has a plethora of implications. In particular, it solves a bijective problem in Stanley's collection "Bijective Proof Problems", and gives a formula for the Narayana polynomials, as well as an equivalent expression for the Harer-Zagier formula enumerating unicellular maps.
Classification : 05A19
Keywords: narayana polynomial, colored tree, Stanley's bijective proof problem, harer- Zagier formula 
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Chen, Ricky X.F.; Reidys, Christian M. A combinatorial identity concerning plane colored trees and its applications. Journal of integer sequences, Tome 20 (2017) no. 3. http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a7/