Lower and upper classes of natural numbers

L. Haddad, Charles 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

Fingerprint

Natural number
Subset
Class
Counting
Partition
Sufficient
Integer

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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
Haddad, L. ; Helou, Charles. / Lower and upper classes of natural numbers. Combinatorial and Additive Number Theory - CANT 2011 and 2012. editor / Melvyn B. Nathanson. Springer New York LLC, 2014. pp. 43-53 (Springer Proceedings in Mathematics and Statistics).
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Haddad, L & Helou, C 2014, Lower and upper classes of natural numbers. in MB Nathanson (ed.), Combinatorial and Additive Number Theory - CANT 2011 and 2012. Springer Proceedings in Mathematics and Statistics, vol. 101, Springer New York LLC, pp. 43-53, School on Combinatorics, Automata and Number Theory, CANT 2012, Marseille, France, 5/21/12. https://doi.org/10.1007/978-1-4939-1601-6_4

Lower and upper classes of natural numbers. / Haddad, L.; Helou, Charles.

Combinatorial and Additive Number Theory - CANT 2011 and 2012. ed. / Melvyn B. Nathanson. Springer New York LLC, 2014. p. 43-53 (Springer Proceedings in Mathematics and Statistics; Vol. 101).

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

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