Skip to main content
SpringerLink
Log in

On An Additive Question

  • Chapter
Number Theory and Discrete Mathematics

  • 107 Accesses

Abstract

Let k > 0 be a given integer. Here we obtain some results concerning solvability of A ⊕ B = ℤk, in B, with respect to a finite set A of a given ‘diameter’. And also announce some other results regarding a conjecture from R. Tijdeman in the case k = 1.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 56.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.M. Coven and A. Meyerowitz, Tiling the Integers with Translates of One Finite Set, J. Algebra 212, 161–174, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.C. Lagarias and Y. Wang, Spectral Sets and Factorizations of Finite Abelian Groups, J. Fund. Anal 145, 73–98, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  3. J.C. Lagarias and S. Szabó, Universal Spectra and Tijdeman’s Conjecture on Factorization of Cyclic Groups. (Preprint: arXiv:math. FA/0008132, 16 Aug 2000; 9 pages.)

    MATH  Google Scholar 

  4. A.D. Sands, On the factorization of finite abelian groups, Acta Math. Acad. Sci. Hungar. 8, 65–86, 1957.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.D. Sands, Replacement of Factors by Subgroups in the Factorization of Abelian Groups, Bull. London Math. Soc. 32, 297–304, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Swenson, Direct sum subset decompositions of ℤ, Pacific J. Math. 53, 629–633, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Tijdeman, Decomposition of the integers as a direct sum of two subsets, in: “Number Theory Seminar Paris 1992–1993)” (S. David, Ed.), pp. 261–276. London Math. Soc. Lecture Note Ser., Vol. 2165, Cambridge Univ. Press, Cambridge, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400 005, India

    S. Srinivasan

Authors
  1. S. Srinivasan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Panjab University, Chandigarh, India

    A. K. Agarwal

  2. Department of Mathematics, Univ. of Illinois at UC Urbana, IL, 61801, USA

    Bruce C. Berndt

  3. Institute of Mathematik, Strudlhof gasse 4 (Strudlhof), A-1090, Wien, Austria

    Christian F. Krattenthaler

  4. “Theorie des Nombers”, Institute de Mathematiques de Jussieu, Case 247, 4, Place, Jussieu, F-75252, Paris Cedex 05, France

    Michel Waldschmidt

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Hindustan Book Agency

About this chapter

Cite this chapter

Srinivasan, S. (2002). On An Additive Question. In: Agarwal, A.K., Berndt, B.C., Krattenthaler, C.F., Mullen, G.L., Ramachandra, K., Waldschmidt, M. (eds) Number Theory and Discrete Mathematics. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-10-1_28

Download citation

Publish with us

Policies and ethics

Search

Navigation