The set A of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. An asymptotic basis of order h is minimal if no proper subset of A is an asymptotic basis of order h. Minimal asymptotic bases are extremal objects in additive number theory, and related to the conjecture of Erdos and Turan that the representation function of an asymptotic basis must be unbounded. This talk describes the construction of a new class of minimal asymptotic bases.
Mel Nathanson