Generalized k-plane trees

Document Type : Full Length Article

Authors

1 Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya

2 Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya.

3 Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya

10.22061/jdma.2025.11859.1122

Abstract

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 1-dimensional plane trees and noncrossing trees are 2-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.

Graphical Abstract

Generalized k-plane trees

Keywords

Main Subjects

Journal of Discrete Mathematics and Its Applications
Volume 10, Issue 2
June 2025
Pages 161-182

Files

History

  • Receive Date: 16 March 2025
  • Revise Date: 25 March 2025
  • Accept Date: 24 April 2025
  • Publish Date: 01 June 2025

Share

How to cite

Statistics