Lev, Vsevolod F. Reconstructing integer sets from their representation functions. (English) Zbl 1068.11006 Electron. J. Comb. 11, No. 1, Research paper R78, 6 p. (2004). First proofs of two theorems of G. Dombi [Acta Arith. 103, No. 2, 137–146 (2002; Zbl 1014.11009)] and Y.-G. Chen and B. Wang [Acta Arith. 110, No. 3, 299–303 (2003; Zbl 1032.11008)] are given.Then the parallel problem for differences is investigated. A set \(A\subseteq\mathbb{Z}\) is a perfect difference set if any integer \(\neq 0\) has a unique representation as a difference of two elements of \(A\). Then the following theorem is proved:There is a partition \(\mathbb{N}=\bigcup^\infty_{k=1} A_k\) such that each \(A_k\) is a perfect difference set and \(|A_i\cap(A_j+ z)|\leq 2\) for any \(i,j,z\in\mathbb{N}\). Reviewer: Erich Härtter (Mainz) Cited in 2 ReviewsCited in 32 Documents MSC: 11B34 Representation functions 05A17 Combinatorial aspects of partitions of integers 11B13 Additive bases, including sumsets Keywords:representation functions; additive bases Citations:Zbl 1014.11009; Zbl 1032.11008 PDFBibTeX XMLCite \textit{V. F. Lev}, Electron. J. Comb. 11, No. 1, Research paper R78, 6 p. (2004; Zbl 1068.11006) Full Text: EuDML EMIS