TY - GEN

T1 - Lower and upper classes of natural numbers

AU - Haddad, L.

AU - Helou, C.

N1 - Publisher Copyright:
© Springer Science+Business Media New York 2014.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84927630040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927630040&partnerID=8YFLogxK

U2 - 10.1007/978-1-4939-1601-6_4

DO - 10.1007/978-1-4939-1601-6_4

M3 - Conference contribution

AN - SCOPUS:84927630040

T3 - Springer Proceedings in Mathematics and Statistics

SP - 43

EP - 53

BT - Combinatorial and Additive Number Theory - CANT 2011 and 2012

A2 - Nathanson, Melvyn B.

PB - Springer New York LLC

T2 - School on Combinatorics, Automata and Number Theory, CANT 2012

Y2 - 21 May 2012 through 25 May 2012

ER -