On leaf related statistics in recursive tree models

Altok, Serdar; Işlak, Ümi̇t

doi:10.1016/j.spl.2016.10.007

Cited by 4 publications

(10 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, again permutation statistics that are related to descents can be understood via independent random variables, though with random words this time. This observation was previously used in [4] and was further developed in [21]. Also, see [20].…”

mentioning

confidence: 74%

A study on random permutation graphs

Gürerk¹,

Işlak²,

Yıldız³

2019

Preprint

View full text Add to dashboard Cite

For a given permutation π n in S n , a random permutation graph is formed by including an edge between two vertices i and j if and only if (i − j)(π n (i) − π n (j)) < 0. In this paper, we study various statistics of random permutation graphs. In particular, we prove central limit theorems for the number m-cliques and cycles of size at least m. Other problems of interest are on the number of isolated vertices, the distribution of a given node (the mid-node as a special case) and extremal degree statistics. Besides, we introduce a directed version of random permutation graphs, and provide two distinct paths that provide variations/generalizations of the model discussed in this paper.

show abstract

mentioning

confidence: 74%

A study on random permutation graphs

Gürerk¹,

Işlak²,

Yıldız³

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…We begin by reviewing constructions of URTs via uniformly random permutations. The discussion here closely follows [1]. In order to construct the URT, we first construct a uniformly random permutation π of {2, 3, .…”

Section: Connections To Random Permutations 21 Urt Constructions Base...mentioning

confidence: 99%

“…That this relation gives a bijection between URTs and uniform random permutations can be seen by the symmetry of the recursive constructions. The tree and the permutation corresponding to it can also be constructed simultaneously, see [1].…”

Section: Connections To Random Permutations 21 Urt Constructions Base...mentioning

confidence: 99%

“…. , i − 1} with probability 1 i−1 [1]. Another way to construct a URT that is useful in understanding certain tree statistics is based on a bijection between recursive trees and permutations.…”

Section: Introductionmentioning

confidence: 99%

“…Variations of recursive trees in non-uniform setting include Hoppe trees [21], weighted recursive trees [20], the binary recursive trees [5], plane-oriented recursive trees [31] and scaled attachment random recursive trees [10]. Our interest here is in yet another model which was recently introduced in [1]. Here, the construction of the random tree is based on a completely different approach using interplay between the symmetric group and recursive trees.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some remarks on biased recursive trees

Hiesmayr,

Işlak

2018

Preprint

View full text Add to dashboard Cite

The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform permutations, biased riffle shuffles. The statistics that are treated include the number of nodes with a given number of descendants, the depth of the tree, and the number of branches. The model yields the uniform recursive trees as a certain limit, some new results for the uniform case are obtained as well.

show abstract

Asymptotic results on Hoppe trees and their variations

Hiesmayr

Işlak

2020

J. Appl. Probab.

View full text Add to dashboard Cite

A uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model more flexible for applications. We analyse the number of leaves, the height, the depth, the number of branches, and the size of the largest branch in these weighted trees.

show abstract

On leaf related statistics in recursive tree models

Cited by 4 publications

References 20 publications

A study on random permutation graphs

A study on random permutation graphs

Some remarks on biased recursive trees

Asymptotic results on Hoppe trees and their variations

Contact Info

Product

Resources

About