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Un conjunto A de enteros se llama conjunto Sidon si todas las sumas de dos elementos en A son distintas; es decir si para todo a, b, c, d ∈ A (a + b = c + d)⇒ {a,b} = {c,d}. Estos conjuntos los consideró el analista Simon Sidon, a principios de los años 1930, en sus investigaciones sobre análisis de Fourier. Una regla Golomb es un conjunto de enteros (no negativos) con la propiedad que todas las diferencias no cero son distintas. Estas reglas especiales aparecieron en el estudio de interferencias en radiofrecuencias, realizado por Wallace Babcock, a principios de los años 1950. En este artículo se realiza un recorrido a través de contextos finitos en los que intervienen estos objetos matemáticos. Los contextos considerados son: conjuntos finitos de números enteros, grupos cíclicos, retículos bidimensionales de coordenadas enteras (arreglos Costas, secuencias Sonar) y funciones APN. En buena parte, estas notas son resultado parcial de actividades realizadas durante mi actual año sabático en la Universidad del Cauca, y son también una versión ampliada de la conferencia invitada, que con el mismo título presenté durante el “55 Congreso Nacional de la Sociedad Matemática Mexicana”, realizado en la Universidad de Guadalajara del 23 al 28 de octubre de 2022 (https://www.smm.org.mx/congreso).
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Derechos de autor 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales