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El Problema de las Estampillas de Correo

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Author(s): Gilberto Garcia Pulgarín | John Hermes Castillo Gómez | Wilson Fernando Mutis Cantero | Fernando Andrés Benavides Agredo

Journal: Revista Sigma
ISSN 2027-064X

Volume: X;
Start page: 18;
Date: 2010;
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Keywords: Postage Stamp Problem | Additive bases

ABSTRACT
Let h a positive integer, A a set of positive integers, with hA we denote the set of all integers representable as a sum of at most h elements of A (allowing repetitions). The Postage Stamp Problem, is to find the largest integer n = n(h,A) such that {1, . . . , n} hA.In this paper we present a new proof of the result of St¨ohr that say how to calculate n(h,A) when A has two elements. From this result we show that if h is a positive integer there exists a set A which is an extremal (, h)−basis and an extremal (, h+ 1)−basis for two stamps.In addition, we find the cases when exist a set which is an extremal (, h)−basis and an extremal (, h + 1)−basis in the case of three stamps.

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