2005/03/15 by William Y. C. Chen, Chen, William Y. C., Louis W. Shapiro +3
Computer Science · Mathematics · #05A15 #05C05 #05C30 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #math.CO #msc:05A15 #msc:05C05 #msc:05C30
paper · pdf · doi:10.48550/arxiv.math/0503300
8 pages, 4 figures
arxiv created 2005/03/15 · openalex publication_date 2005/03/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schröder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.