Bijections between certain families of labelled and unlabelled d-ary trees

Panholzer, Alois; Prodinger, Helmut

doi:10.2298/aadm0901123p

Search citation statements

Order By: Relevance

Paper Sections

Select...

Discussion1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2023

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, k such that if the rightmost child has label j and its parent label i then i ≤ j. These trees were introduced and studied by Panholzer and Prodinger in [11].…”

Section: Discussionmentioning

confidence: 99%

Reachability in complete t-ary trees

Abayo,

Okoth,

Kasyoki

2023

AMCS

View full text Add to dashboard Cite

Mathematical trees such as Cayley trees, plane trees, binary trees, noncrossing trees, t-ary trees among others have been studied extensively. Reachability of vertices as a statistic has been studied in Cayley trees, plane trees, noncrossing trees and recently in t-ary trees where all edges are oriented from vertices of lower label towards vertices of higher label. In this paper, we obtain closed formulas as well as asymptotic formulas for the number of complete t-ary trees in which there are paths of a given length such that the terminal vertex is a sink, leaf sink, first child and non-first child. We also obtain number of trees in which there is a leftmost path of a given length.

show abstract

“…, k such that if the rightmost child has label j and its parent label i then i ≤ j. These trees were introduced and studied by Panholzer and Prodinger in [11].…”

Section: Discussionmentioning

confidence: 99%

Reachability in complete t-ary trees

Abayo,

Okoth,

Kasyoki

2023

AMCS

View full text Add to dashboard Cite

show abstract

“…Mansour et al [1] in 2008 mentioned that -free two colored binary trees are hybrid binary trees, and considered several types of "X-free" bicolored binary trees and enumerated them. In 2009, Panholzer and Prodinger [4] studied d-ary trees with no rightmost -edges and found a closed formula as a generalized Catalan numbers. They also enumerate k colored d-ary trees with {1, 2, .…”

Section: Introductionmentioning

confidence: 99%