Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21287220221201Enumeration of k-noncrossing trees and forests3013111435310.22049/cco.2022.26903.1162ENIsaac OwinoOkothDepartment of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya0000-0003-4503-4733Journal Article20200809A $k$-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 $k$.http://comb-opt.azaruniv.ac.ir/article_14353_690e707a9886b43c3feb284d6b4c5f5a.pdf