IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-2418-1_15.html
   My bibliography  Save this book chapter

Minimal Bases and g-Adic Representations of Integers

In: Number Theory: New York Seminar 1991–1995

Author

Listed:
  • Xing-De Jia

    (Southwest Texas State University, Department of Mathematics)

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

Suggested Citation

  • Xing-De Jia, 1996. "Minimal Bases and g-Adic Representations of Integers," Springer Books, in: David V. Chudnovsky & Gregory V. Chudnovsky & Melvyn B. Nathanson (ed.), Number Theory: New York Seminar 1991–1995, chapter 15, pages 201-209, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2418-1_15
    DOI: 10.1007/978-1-4612-2418-1_15
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4612-2418-1_15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.