Abstract
Let N denote the set of all nonnegative integers and A be a subset of N. Let h be an integer with h≥2. Let n∈N and rh(A,n)=♯{(a1,…,ah)∈Ah:a1+⋯+ah=n}. The set A is called an asymptotic basis of order h if rh(A,n)≥1 for all sufficiently large integer n. An asymptotic basis A of order h is minimal if no proper subset of A is an asymptotic basis of order h. In 1988, Nathanson posed a problem on minimal asymptotic bases of order h. Recently, Chen and Tang showed that the answer to the problem is negative for h≥4 by constructing a special partition of N. In this paper, we give a new construction of minimal asymptotic bases. This construction expands our understanding on the problem of Nathanson.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.