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
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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 -