g-Golomb Rulers

YADIRA CAICEDO^{a *}, CARLOS A. MARTOS^b , CARLOS A. TRUJILLO^b

^aUniversidad del Tolima, Departamento de Matemáticas y Estadística, Ibagué, Colombia.

^bUniversidad del Cauca, Departamento de Matemáticas, Popayán, Colombia.

Abstract. A set of positive integers A is called a g-Golomb ruler if the difference between two distinct elements of A is repeated at most g times. This definition is a generalization of the Golomb ruler (g = 1). In this paper we construct g-Golomb ruler from Golomb ruler and we prove two theorems about extremal functions associated with this sets.

Keywords: Sidon sets, B₂ sets, Golomb ruler.
MSC2010: 11B50, 12E20, 20K01, 20K30.

Reglas g-Golomb

Resumen. Se dice que un conjunto de enteros positivos A satisface la regla g-Golomb si la diferencia entre dos elementos distintos de A se repite a lo más g veces. Esta definición es una generalización de las reglas de Golomb (g = 1). En este artículo construimos reglas g-Golomb a partir de reglas Golomb y demostramos dos teoremas sobre las funciones extremas asociadas con estos conjuntos.

Palabras clave: Conjuntos de Sidon, conjuntos B₂, reglas Golomb.

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*E-mail: nycaicedob@ut.edu.co.
Received: 31 July 2015, Accepted: 10 November 2015.
To cite this article: Y. Caicedo, C.A. Martos, C.A. Trujillo, g-Golomb, Rev. Integr. Temas Mat. 33 (2015), No. 2, 161-172.