@article{Article_97,

title = {Enumeration of a variant of k-noncrossing trees},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2025},

issue = {1},

issn = { 2783-5456 },

year = {2025},

url = {http://cccs.sgh.ac.ir/Articles/2025/issue 1/1-1-Enumerationofavariantofknoncrossingtrees.pdf},

author = {Fidel Ochieng Oduol and Isaac Owino Okoth and Fredrick Oluoch Nyamwala},

keywords = {k1-noncrossing tree, root degree, eldest child, youngest child, forest.},

abstract = {In this paper, a variant of k-noncrossing trees where all children (labelled 1) of all internal nodes in the (l, r)-representation of the noncrossing trees must be on the left of all others is introduced and enumerated by number of nodes, root degree, labels of the eldest child or youngest child of the root, length of the leftmost path and forests. Generating functions, symbolic method, right substitutions and Lagrange-Bürmann inversion are applied to obtain the results. Known results for noncrossing trees and nondecreasing 2-noncrossing trees follow as corollaries.}

};