A simple proof that any additive basis has only finitely many essential subsets

Details A simple proof that any additive basis has only finitely many essential subsets A simple proof that any additive basis has only finitely many essential subsets

2008-07-22

arxiv.org/abs/0807.3461v2

Mathematics

Number Theory

3 pages

Scientific paper

Let $A$ be an additive basis. We call ``essential subset'' of $A$ any finite subset $P$ of $A$ such that $A \setminus P$ is not an additive basis and that $P$ is minimal (for the inclusion order) to have this property. A recent theorem due to B. Deschamps and the author states that any additive basis has only finitely many essential subsets (see ``Essentialit\'e dans les bases additives, J. Number Theory, 123 (2007), p. 170-192''). The aim of this note is to give a simple proof of this theorem.

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