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• W4200318269 abstract "For a nonempty set A of integers and any integer n, denote rA(n) by the number of representations of n of the form n=a+a′, where a⩽a′ and a,a′∈A and dA(n) by the number of pairs (a,a′) with a,a′∈A such that n=a−a′. In 2008, Nathanson considered the representation function with infinitely many zeros. In this paper, as a main result, we prove that, for any set T of integers with density zero, there exists a sequence A of integers such that rA(n)=1 for all integers n⁄∈T and rA(n)=0 for all integers n∈T, and dA(n)=1 for all positive integers n. Other result about restricted representation function is also obtained." @default.
• W4200318269 created "2021-12-31" @default.
• W4200318269 creator A5046981773 @default.
• W4200318269 date "2022-05-01" @default.
• W4200318269 modified "2023-10-16" @default.
• W4200318269 title "Representation functions avoiding integers with density zero" @default.
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• W4200318269 doi "https://doi.org/10.1016/j.ejc.2021.103490" @default.
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