Divisibility Patterns within Pascal Divisibility Networks
by
Pedro A. Solares-Hernández 1,2, Fernando A. Manzano 1,2, Francisco J. Pérez-Benito 1,3
and 
J. Alberto Conejero 1,*
Pedro A. Solares-Hernández 1,2, Fernando A. Manzano 1,2, Francisco J. Pérez-Benito 1,3 and J. Alberto Conejero 1,*
1
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, Spain
2
Departamento de Estadística, Universidad APEC, 10203 Santo Domingo, Dominican Republic 3 Instituto de Tecnología Informática (ITACA), Universitat Politècnica de València, 91354 València, Spain
3
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.
Keywords:
network science; graph theory; divisibility; Pascal matrix
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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.
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