Parity reversing involutions on plane trees and 2-Motzkin paths
نویسندگان
چکیده
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 of sets was independently studied by Klazar. We present three parity reversing involutions for the identity, the first is stated in terms of unlabelled plane trees, the second is formulated by labelled plane trees and the third is described by 2-Motzkin paths. AMS Classification: 05A15, 05C30, 05C05
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عنوان ژورنال:
- Eur. J. Comb.
دوره 27 شماره
صفحات -
تاریخ انتشار 2006