Divisibility Patterns within Pascal Divisibility Networks
1
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
2
Departamento de Estadística, Universidad APEC, Santo Domingo 10203, Dominican Republic
3
Departamento de Ingeniería, Universidad APEC, Santo Domingo 10203, Dominican Republic
4
Instituto de Tecnología Informática (ITACA), Universitat Politècnica de València, 91354 València, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 254; https://doi.org/10.3390/math8020254
Received: 31 December 2019 / Revised: 3 February 2020 / Accepted: 7 February 2020 / Published: 14 February 2020
(This article belongs to the Section Network Science)
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.
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Keywords:
network science; graph theory; divisibility; Pascal matrix
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MDPI and ACS Style
Solares-Hernández, P.A.; Manzano, F.A.; Pérez-Benito, F.J.; Conejero, J.A. Divisibility Patterns within Pascal Divisibility Networks. Mathematics 2020, 8, 254. https://doi.org/10.3390/math8020254
AMA Style
Solares-Hernández PA, Manzano FA, Pérez-Benito FJ, Conejero JA. Divisibility Patterns within Pascal Divisibility Networks. Mathematics. 2020; 8(2):254. https://doi.org/10.3390/math8020254
Chicago/Turabian StyleSolares-Hernández, Pedro A.; Manzano, Fernando A.; Pérez-Benito, Francisco J.; Conejero, J. A. 2020. "Divisibility Patterns within Pascal Divisibility Networks" Mathematics 8, no. 2: 254. https://doi.org/10.3390/math8020254
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