TY - JOUR
ID - 14353
TI - Enumeration of k-noncrossing trees and forests
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Okoth, Isaac Owino
AD - Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya
Y1 - 2022
PY - 2022
VL - 7
IS - 2
SP - 301
EP - 311
KW - noncrossing trees
KW - degree
KW - forest
DO - 10.22049/cco.2022.26903.1162
N2 - 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 $k$.
UR - http://comb-opt.azaruniv.ac.ir/article_14353.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14353_690e707a9886b43c3feb284d6b4c5f5a.pdf
ER -