Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

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dc.creatorChen, William Y. C.
dc.creatorShapiro, Louis W.
dc.creatorYang, Laura L. M.
dc.date2005-03-15
dc.date.accessioned2026-07-07T05:17:58Z
dc.date.available2026-07-07T05:17:58Z
dc.descriptionThe 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.
dc.description8 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0503300
dc.identifierhttp://arxiv.org/abs/math/0503300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74502
dc.subjectCombinatorics
dc.subject05A15, 05C30, 05C05
dc.titleParity Reversing Involutions on Plane Trees and 2-Motzkin Paths
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