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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Vydané v:Discrete mathematics Ročník 340; číslo 6; s. 1154 - 1161
Hlavní autori: Kiss, Sándor Z., Sándor, Csaba
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.06.2017
Predmet:
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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Abstract 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.
AbstractList 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.
Author Sándor, Csaba
Kiss, Sándor Z.
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Cites_doi 10.1016/j.disc.2007.06.006
10.37236/1831
10.1016/j.jnt.2009.04.020
10.4064/aa103-2-3
10.1007/s11425-011-4234-5
10.1016/j.disc.2014.11.011
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Keywords Representation functions
Partitions of the set of natural numbers
Additive number theory
Language English
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References Chen, Wang (b4) 2003; 113
Lev (b6) 2004; 11
Tang (b9) 2008; 308
Tang (b10) 2016; 37
Chen, Tang (b3) 2009; 129
Tang, Yu (b11) 2012; 12
Chen, Lev (b2) 2016; 16
Sándor (b8) 2004; 4
Chen (b1) 2011; 54
Qu (b7) 2015; 338
Dombi (b5) 2002; 103
Lev (10.1016/j.disc.2017.01.011_b6) 2004; 11
Tang (10.1016/j.disc.2017.01.011_b11) 2012; 12
Chen (10.1016/j.disc.2017.01.011_b1) 2011; 54
Chen (10.1016/j.disc.2017.01.011_b2) 2016; 16
Tang (10.1016/j.disc.2017.01.011_b9) 2008; 308
Tang (10.1016/j.disc.2017.01.011_b10) 2016; 37
Qu (10.1016/j.disc.2017.01.011_b7) 2015; 338
Chen (10.1016/j.disc.2017.01.011_b4) 2003; 113
Dombi (10.1016/j.disc.2017.01.011_b5) 2002; 103
Chen (10.1016/j.disc.2017.01.011_b3) 2009; 129
Sándor (10.1016/j.disc.2017.01.011_b8) 2004; 4
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Snippet 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...
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Partitions of the set of natural numbers
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Title Partitions of the set of nonnegative integers with the same representation functions
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