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Divisibility Patterns within Pascal Divisibility Networks

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  • Pedro A. Solares-Hernández

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
    Departamento de Estadística, Universidad APEC, Santo Domingo 10203, Dominican Republic
    Departamento de Ingeniería, Universidad APEC, Santo Domingo 10203, Dominican Republic)

  • Fernando A. Manzano

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
    Departamento de Estadística, Universidad APEC, Santo Domingo 10203, Dominican Republic
    Departamento de Ingeniería, Universidad APEC, Santo Domingo 10203, Dominican Republic)

  • Francisco J. Pérez-Benito

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
    Instituto de Tecnología Informática (ITACA), Universitat Politècnica de València, 91354 València, Spain)

  • J. Alberto Conejero

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain)

Abstract

The Pascal triangle is so simple and rich that it has always attracted the interest of professional and amateur mathematicians. Their coefficients satisfy a myriad of properties. Inspired by the work of Shekatkar et al., we study the divisibility patterns within the elements of the Pascal triangle, through its decomposition into Pascal’s matrices, from the perspective of network science. Applying Kolmogorov–Smirnov test, we determine that the degree distribution of the resulting network follows a power-law distribution. We also study degrees, global and local clustering coefficients, stretching graph, averaged path length and the mixing assortative.

Suggested Citation

  • Pedro A. Solares-Hernández & Fernando A. Manzano & Francisco J. Pérez-Benito & J. Alberto Conejero, 2020. "Divisibility Patterns within Pascal Divisibility Networks," Mathematics, MDPI, vol. 8(2), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:254-:d:320856
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    References listed on IDEAS

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    1. Gillespie, Colin S., 2015. "Fitting Heavy Tailed Distributions: The poweRlaw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i02).
    2. Zhou, Tao & Wang, Bing-Hong & Hui, P.M. & Chan, K.P., 2006. "Topological properties of integer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 613-618.
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    1. Carmen Moret-Tatay & Inmaculada Baixauli-Fortea & M. Dolores Grau Sevilla & Tatiana Quarti Irigaray, 2020. "Can You Identify These Celebrities? A Network Analysis on Differences between Word and Face Recognition," Mathematics, MDPI, vol. 8(5), pages 1-17, May.

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