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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Vydáno v:Discrete mathematics Ročník 340; číslo 6; s. 1154 - 1161
Hlavní autoři: Kiss, Sándor Z., Sándor, Csaba
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2017
Témata:
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
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Shrnutí: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