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Refined enumeration of k-plane trees and k-noncrossing trees
(2022)
A k-plane tree is a plane tree whose vertices are assigned labels between 1 and k in such a way that the sum of the labels along any edge is no greater than k+1. These trees are known to be related to (k+1)-ary trees, and ...
Bijections of k-plane trees
(Open journal of discrete Applied Mathematics, 2022)
A k-plane tree is a tree drawn in the plane such that the vertices are labeled by integers in the set
{1, 2, . . . , k}, the children of all vertices are ordered, and if (i, j) is an edge in the tree, where i and j are ...