Abstract
We consider a partition of the subsets of the natural numbers \(\mathbb{N}\) into two classes, the lower class and the upper class, according to whether the representation function of such a subset A, counting the number of pairs of elements of A whose sum is equal to a given integer, is bounded or unbounded. We give sufficient criteria for two subsets of \(\mathbb{N}\) to be in the same class and for a subset to be in the lower class or in the upper class.
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Acknowledgements
We would like to thank G. Grekos and J. Pihko, who contributed to some of the above results, which appeared in other venues, as indicated in the bibliography.
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Haddad, L., Helou, C. (2014). Lower and Upper Classes of Natural Numbers. In: Nathanson, M. (eds) Combinatorial and Additive Number Theory. Springer Proceedings in Mathematics & Statistics, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1601-6_4
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DOI: https://doi.org/10.1007/978-1-4939-1601-6_4
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