Independence of solution sets and minimal asymptotic bases
نویسندگان
چکیده
(4) 0 < a1 < a2 < . . . < ak and ai ∈ A for i = 1, . . . , k. The set A is called an asymptotic basis of order k if there exists a natural number n1 such that rA(n) > 0 for all n ≥ n1. The set A is called a strict asymptotic basis of order k if there exists a natural number n1 such that r′ A(n) > 0 for all n ≥ n1. All bases considered in this paper will be either asymptotic or strict asymptotic bases of order k. Erdős and Tetali [7] gave a probabilistic construction of a strict asymptotic basis S of order k whose representation function satisfies log n r′ S(n) logn. An asymptotic basis (resp. strict asymptotic basis) A is called minimal if the removal of any element from the basis destroys all representations of some infinite sequence of numbers, that is, A \ {a} is not an asymptotic
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