IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v52y2021i4d10.1007_s13226-021-00089-6.html
   My bibliography  Save this article

On a sumset problem of dilates

Author

Listed:
  • Sandeep Singh Chahal

    (Akal University)

  • Ram Krishna Pandey

    (Indian Institute of Technology Roorkee)

Abstract

Let A be a nonempty finite set of integers. For a real number m, the set $$m\cdot A=\{ma: a\in A\}$$ m · A = { m a : a ∈ A } denotes the set of m-dilates of A. In 2008, Bukh initiated an interesting problem of finding a lower bound for the sumset of dilated sets, i.e., a lower bound for $$|m_1\cdot A+m_2\cdot A+ \cdots +m_n\cdot A|$$ | m 1 · A + m 2 · A + ⋯ + m n · A | , where $$m_1, m_2, \ldots , m_n$$ m 1 , m 2 , … , m n are integers. In this paper, we consider the case $$|3\cdot A+k\cdot A|$$ | 3 · A + k · A | , where k is a prime number $$\ge 5$$ ≥ 5 . Under some assumptions on A, first we give a general lower bound on the cardinality of $$3\cdot A+k\cdot A$$ 3 · A + k · A then, for large sets A, under the same assumptions, we improve this general lower bound. The results also hold true for the general sumset $$q \cdot A + k\cdot A$$ q · A + k · A , where q is any odd prime $$

Suggested Citation

  • Sandeep Singh Chahal & Ram Krishna Pandey, 2021. "On a sumset problem of dilates," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 1180-1185, December.
  • Handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00089-6
    DOI: 10.1007/s13226-021-00089-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-021-00089-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13226-021-00089-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Additive combinatorics; Sumsets of dilates;

    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:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00089-6. 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.