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On the structure of some sets which have the same representation functions

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Abstract

Let \(\mathbb {N}\) be the set of nonnegative integers. For a given set \(S\subset \mathbb {N}\) the representation function \(R_S(n)\) is defined as the number of solutions of the equation \(n=s+s', s<s', s,s'\in S\). In this paper, we characterize some sets which have the same representation functions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, People’s Republic of China

    Min Tang & Jia-Wen Li

Authors
  1. Min Tang
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  2. Jia-Wen Li
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Correspondence to Min Tang.

Additional information

This work was supported by National Natural Science Foundation of China, Grant No. 11471017.

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Tang, M., Li, JW. On the structure of some sets which have the same representation functions. Period Math Hung 77, 232–236 (2018). https://doi.org/10.1007/s10998-018-0240-5

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  • DOI: https://doi.org/10.1007/s10998-018-0240-5

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