Minimal Bases and g-Adic Representations of Integers

Xing- De Jia
Additional contact information
Xing- De Jia: Southwest Texas State University, Department of Mathematics

Chapter 15 in Number Theory: New York Seminar 1991–1995, 1996, pp 201-209 from Springer

Abstract: Abstract Let A be a set of integers, h ≥ 2 an integer. Let hA denote the set of all sums of h elements of A. If hA contains all sufficiently large integers, then A is called an asymptotic basis of order h. An asymptotic basis A of order h is said to be minimal if it contains no proper subset which is again an asymptotic basis of order h. This concept of minimality of bases was first introduced by Stöhr [5]. Härtter [1] showed the existence of minimal asymptotic bases by a nonconstructive argument. Nathanson [3] constructed the first nontrivial example of minimal asymptotic bases of order h ≥ 2. Jia and Nathanson [2] recently discovered a simple construction of minimal asymptotic bases of order h ≥ 2 by using powers of 2. Furthermore, for any α: 1/h ≤; α

Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2418-1_15

Ordering information: This item can be ordered from
http://www.springer.com/9781461224181

DOI: 10.1007/978-1-4612-2418-1_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().