@article {
author = {Okoth, Isaac},
title = {Enumeration of k-noncrossing trees and forests},
journal = {Communications in Combinatorics and Optimization},
volume = {7},
number = {2},
pages = {301-311},
year = {2022},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2022.26903.1162},
abstract = {A $k$-noncrossing tree is a noncrossing tree where each node receives a label in $\{1,2,\ldots,k\}$ such that the sum of labels along an ascent does not exceed $k+1,$ if we consider a path from a fixed vertex called the root. In this paper, we provide a proof for a formula that counts the number of $k$-noncrossing trees in which the root (labelled by $k$) has degree $d$. We also find a formula for the number of forests in which each component is a $k$-noncrossing tree whose root is labelled by $k$.},
keywords = {noncrossing trees,degree,forest},
url = {http://comb-opt.azaruniv.ac.ir/article_14353.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14353_690e707a9886b43c3feb284d6b4c5f5a.pdf}
}