Partitions of the set of nonnegative integers with the same representation functions

For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the integer n as the sum of two different terms from S. In this paper we focus on partitions of the natural numbers into two sets affording identical representation functions. We solve a recent problem of...

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Bibliographic Details
Published in:	Discrete mathematics Vol. 340; no. 6; pp. 1154 - 1161
Main Authors:	Kiss, Sándor Z., Sándor, Csaba
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.06.2017
Subjects:	Additive number theory Partitions of the set of natural numbers Representation functions Representation functions Partitions of the set of natural numbers Additive number theory
ISSN:	0012-365X, 1872-681X
Online Access:	Get full text
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Summary:	For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the integer n as the sum of two different terms from S. In this paper we focus on partitions of the natural numbers into two sets affording identical representation functions. We solve a recent problem of Chen and Lev.
ISSN:	0012-365X 1872-681X
DOI:	10.1016/j.disc.2017.01.011