3 papers
math.NT2025
On the Sierpinski triangle and its generalizations
L. De Carli, A. Echezabal, I. Morell
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle
math.NT2024
Egyptian fractions meet the Sierpinski triangle
Laura De Carli, Andrew Echezabal, Ismael Morell
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct un…
math.NT2023
Approximating the divisor functions
Andrew Echezabal, Laura De Carli, Maurizio Laporta
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof…