Lower and upper classes of natural numbers

L. Haddad, C. Helou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a partition of the subsets of the natural numbers 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 ℕ to be in the same class and for a subset to be in the lower class or in the upper class.

Original languageEnglish (US)
Title of host publicationCombinatorial and Additive Number Theory - CANT 2011 and 2012
EditorsMelvyn B. Nathanson
PublisherSpringer New York LLC
Pages43-53
Number of pages11
ISBN (Electronic)9781493916009
DOIs
StatePublished - Jan 1 2014
EventSchool on Combinatorics, Automata and Number Theory, CANT 2012 - Marseille, France
Duration: May 21 2012May 25 2012

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume101
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherSchool on Combinatorics, Automata and Number Theory, CANT 2012
CountryFrance
CityMarseille
Period5/21/125/25/12

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Haddad, L., & Helou, C. (2014). Lower and upper classes of natural numbers. In M. B. Nathanson (Ed.), Combinatorial and Additive Number Theory - CANT 2011 and 2012 (pp. 43-53). (Springer Proceedings in Mathematics and Statistics; Vol. 101). Springer New York LLC. https://doi.org/10.1007/978-1-4939-1601-6_4