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Generalized difference sets on an infinite cyclic semigroup. (English) Zbl 0777.05025
Let \(\{\lambda_ i\}\) \((i\in\mathbb{N})\) be a nondecreasing sequence of elements of \(\mathbb{N}\). The authors give a recursive construction of a set \(G\) such that, for every \(i\in\mathbb{N}\), there are precisely \(\lambda_ i\) solutions of the equation \(i+g=h\) (in \(\langle g,h\rangle\), with \(g,h\in G)\). Some other interesting developments are given or suggested.
Reviewer: G.Ferrero (Parma)

MSC:
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
20M99 Semigroups
11B83 Special sequences and polynomials
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