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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
##### Keywords:
difference sets; cyclic semigroup; sequence