Geodesic
A combinatorial identity concerning plane colored trees and its applications
Journal of integer sequences, Tome 20 (2017) no. 3
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 
@article{JIS_2017__20_3_a7,
     author = {Chen,  Ricky X.F. and Reidys,  Christian M.},
     title = {A combinatorial identity concerning plane colored trees and its applications},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {3},
     zbl = {1355.05045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a7/}
}
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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/