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Kenneth Omondi Lumumba, Isaac Owino Okoth and Donnie Munyao Kasyoki, Refined enumeration of 2-plane trees, Eur. J. Math. Appl. 5 (2025), Article ID 8.

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Volume 5 (2025), Article ID 8

https://doi.org/10.28919/ejma.2025.5.8

Published: 10/02/2025

Abstract:

Plane trees and their generalizations have been widely studied. One such generalization is by assigning labels to the vertices of plane trees such that the sum of labels of the endpoints of each edge satisfy a certain condition. Gu, Prodinger and Wagner introduced and enumerated 2-plane trees which are plane trees with vertices coloured either white or black such that there are no black-black edges. In this paper, 2-plane trees are enumerated according to the colour of the first child of the root, degree of the root and level of a vertex of a given colour and degree. The counting formulas are obtained by means of symbolic method to obtain the generating functions and making use of Lagrange inversion formula, bijections and decomposition of trees so as to use Rothe-Hagen identity which is a generalization of Vandermonde identity.

How to Cite:

Kenneth Omondi Lumumba, Isaac Owino Okoth and Donnie Munyao Kasyoki, Refined enumeration of 2-plane trees, Eur. J. Math. Appl. 5 (2025), Article ID 8. https://doi.org/10.28919/ejma.2025.5.8