6 citations · 16 across the 8 of their papers we have counts for
8 papers
Characterization of Trees with Maximum Security
Alex S. A. Alochukwu, Audace A. V. Dossou-Olory, Fadekemi J. Osaye +5
The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the s…
The distribution of the maximum protection number in simply generated trees
Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner
The protection number of a vertex in a tree is the length of the shortest path from to any leaf contained in the maximal subtree where is the root. In this paper, we de…
Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo
Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner
For fixed non-negative integers , , and , with , a -Dyck path of length is a lattice path that starts at , ends at , stays weakly…
Down-step statistics in generalized Dyck paths
Andrei Asinowski, Benjamin Hackl, Sarah J. Selkirk
The number of down-steps between pairs of up-steps in -Dyck paths, a generalization of Dyck paths consisting of steps such that the path stays (weakly) a…
Sums of squares of Tetranacci numbers: A generating function approach
Helmut Prodinger, Sarah J. Selkirk
It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provid…
On two subclasses of Motzkin paths and their relation to ternary trees
Helmut Prodinger, Sarah J. Selkirk, Stephan Wagner
Two subclasses of Motzkin paths, S-Motzkin and T-Motzkin paths, are introduced. We provide bijections between S-Motzkin paths and ternary trees, S-Motzkin paths and non-crossing tr…
A bijection between ternary trees and a subclass of Motzkin paths
Helmut Prodinger, Sarah J. Selkirk
A bijection between ternary trees with nodes and a subclass of Motzkin paths of length is given. This bijection can then be generalized to -ary trees.
A closed formula for the generating function of -Bernoulli numbers: An elementary proof
Helmut Prodinger, Sarah J. Selkirk
For a two parameter family of Bernoulli numbers the exponential generating function is derived by elementary methods.