Asymptotic nonbases which are not subsets of maximal asymptotic nonbases

Abstract

Let A be a set of positive integers. If all but a finite number of the positive integers can be written as a sum of h elements of A, then A is called an asymptotic basis of order h. Otherwise, A is called an asymptotic nonbasis of order h. For each h ⩾ 2 h \geqslant 2 , we construct an asymptotic nonbasis of order h which is not a subset of a maximal asymptotic nonbasis of order h.