Rooted tree statistics from Matula numbers

Deutsch, Emeric

doi:10.1016/j.dam.2012.05.012

Cited by 6 publications

(4 citation statements)

References 24 publications

(25 reference statements)

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“…A number of articles have been published on diverse correspondences and other relations between trees and natural numbers, such as [12], [13], [14], [15], [16], [17] and [18], but these studies do not focus specifically on binary trees.…”

Section: Introductionmentioning

confidence: 99%

A One-to-One Correspondence between Natural Numbers and Binary Trees

Skliar,

Gapper,

Monge

2020

Preprint

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A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.

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Section: Introductionmentioning

confidence: 99%

A One-to-One Correspondence between Natural Numbers and Binary Trees

Skliar,

Gapper,

Monge

2020

Preprint

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“…In 2012, Deutsch [10] showed how to determine further properties (mostly distancebased) of a rooted tree directly from the corresponding Matula number. As such, we have the path length, number of subtrees, Wiener index, terminal Wiener index, Wiener polynomial, first Zagreb index, second Zagreb index, just to mention a few.…”

Section: Introductionmentioning

confidence: 99%

The topological trees with extreme Matula numbers

Dossou-Olory

2018

Preprint

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Let T be a rooted tree with branches T 1 , T 2 , . . . , T r and p m the m-th prime number (p 1 = 2, p 2 = 3, p 3 = 5, . . .). The Matula number M (T ) of T is p M (T1) •p M (T2) •. . .• p M (Tr) , starting with M (•) = 1. It was put forward half a century ago by the American mathematician David Matula. In this paper, we prove that the star (consisting of a root and leaves attached to it) and the binary caterpillar (a binary tree whose internal vertices form a path starting at the root) have the smallest and greatest Matula number, respectively, over all topological trees (rooted trees without vertices of outdegree 1) with a prescribed number of leaves -the extremal values are also derived.

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“…Number theoretic aspects of this rooted tree coding have been investigated in detail in [1,13]. Such numbers may be used to deduce many intrinsic properties of rooted trees [4,12,15]. The set A 2 in fact corresponds to a class of Matula numbers.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic distribution of integers with certain prime factorizations

Vernaeve

Vindas

Weiermann

2014

Journal of Number Theory

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Abstract. Let p 1 < p 2 < · · · < p ν < · · · be the sequence of prime numbers and let m be a positive integer. We give a strong asymptotic formula for the distribution of the set of integers having prime factorizations of the form p m k 1 p m k 2 · · · p m kn with k 1 ≤ k 2 ≤ · · · ≤ k n . Such integers originate in various combinatorial counting problems; when m = 2, they arise as Matula numbers of certain rooted trees.

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Rooted tree statistics from Matula numbers

Abstract: There is a one-to-one correspondence between natural numbers and rooted trees; the number is called the Matula number of the rooted tree. We show how a large number of properties of trees can be obtained directly from the corresponding Matula number. arXiv:1111.4288v1 [math.CO]

Cited by 6 publications

References 24 publications

A One-to-One Correspondence between Natural Numbers and Binary Trees

A One-to-One Correspondence between Natural Numbers and Binary Trees

The topological trees with extreme Matula numbers

Asymptotic distribution of integers with certain prime factorizations

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