Estimation of the number of exceptions that a basis set reduced by one point remains a basis set. (Estimation du nombre d’exceptions à ce qu’un ensemble de base privé d’un point reste un ensemble de base.) (English) Zbl 1002.11011
A set \(B\subset \mathbb{N}\) is said to be a basis set of order \(h\) if the set \(\mathbb{N}\setminus (hB)\) is finite. Let \(A\) be a basis set of order \(h\), and put \(A_0=\{a\in A : (A\setminus a)\) is not a basis set}. The authors show that the cardinality of \(A_0\) is \(\leq 5.7\sqrt{\frac{h}{\log h}}\).
Reviewer: Y.O.Hamidoune (Paris)
