A Combinatorial Identity Concerning Plane Colored Trees and its Applications
Ricky X. F. Chen and Christian M. Reidys
Biocomplexity Institute and Department of Mathematics
Virginia Polytechnic Institute and State University
1015 Life Science Circle
Blacksburg, VA 24061
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.
Full version: pdf,
(Concerned with sequences
Received September 13 2016; revised versions received January 18 2017; January 23 2017;
January 25 2017.
Published in Journal of Integer Sequences, January 26 2017.
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