Generalized k-plane trees

Plane trees and noncrossing trees have been generalized by assigning labels to the vertices from a given set such that a prior coherence condition is satisfied. These trees are called k-plane trees and k-noncrossing trees respectively if k labels are used. Results of plane trees and noncrossing trees were recently unified by considering d-dimensional plane trees where plane trees are ۱-dimensional plane trees and noncrossing trees are ۲-dimensional plane trees. In this paper, d-dimensional k-plane trees are introduced and enumerated according to number of vertices and label of the root, root degree, number of components constituting a forest, label of the eldest child of the root and the length of the leftmost path. The equivalent results for plane trees and noncrossing trees follow easily from our results as corollaries.

کلیدواژه ها:

d-dimensional ، root degree ، forest ، eldest child ، leftmost path