Geodesic
Reconstructing integer sets from their representation functions
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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We give a simple common proof to recent results by Dombi and by Chen and Wang concerning the number of representations of an integer in the form $a_1+a_2$, where $a_1$ and $a_2$ are elements of a given infinite set of integers. Considering the similar problem for differences, we show that there exists a partition ${\Bbb N}=\cup_{k=1}^\infty A_k$ of the set of positive integers such that each $A_k$ is a perfect difference set (meaning that any non-zero integer has a unique representation as $a_1-a_2$ with $a_1,a_2\in A_k$). A number of open problems are presented.
DOI : 10.37236/1831
Classification : 11B34, 05A17, 11B13
Mots-clés : representation functions, additive bases 
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     author = {Vsevolod F. Lev},
     title = {Reconstructing integer sets from their representation functions},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1831},
     zbl = {1068.11006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1831/}
}
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Vsevolod F. Lev. Reconstructing integer sets from their representation functions. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1831

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