Lower and upper classes of natural numbers

L. Haddad, C. Helou

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


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
Number of pages11
ISBN (Electronic)9781493916009
StatePublished - 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
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


OtherSchool on Combinatorics, Automata and Number Theory, CANT 2012

All Science Journal Classification (ASJC) codes

  • General Mathematics


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