%0 Journal Article
%T Enumeration of k-noncrossing trees and forests
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Okoth, Isaac Owino
%D 2022
%\ 12/01/2022
%V 7
%N 2
%P 301-311
%! Enumeration of k-noncrossing trees and forests
%K noncrossing trees
%K degree
%K forest
%R 10.22049/cco.2022.26903.1162
%X 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 $k$.
%U http://comb-opt.azaruniv.ac.ir/article_14353_690e707a9886b43c3feb284d6b4c5f5a.pdf