Oscillations of bases in number theory and combinatorics

  • Melvyn B. Nathanson
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 626)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Deza and P. Erdös, Extension de quelques theoremes sur les densities de series d'elements de N a des series de sous-ensembles finis de N, Discrete Math. 12(1975), 295–308.MathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Erdös and M. B. Nathanson, Maximal asymptotic nonbases, Proc. Amer. Math. Soc. 48(1975), 57–60.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P. Erdös and M. B. Nathanson, Oscillations of bases for the natural numbers, Proc. Amer. Math. Soc. 53(1975), 253–258.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    P. Erdös and M. B. Nathanson, Partitions of the natural numbers into infinitely oscillating bases and nonbases, Comment. Math. Helvet. 51(1976), 171–182.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    P. Erdös and M. B. Nathanson, Nonbases of density zero not contained in maximal nonbases, J. London Math. Soc. 15(1977).Google Scholar
  6. 6.
    P. Erdös and M. B. Nathanson, Bases and nonbases of square-free integers, preprint.Google Scholar
  7. 7.
    R. L. Graham, H. W. Lenstra, Jr., and C. L. Stewart, personal communication.Google Scholar
  8. 8.
    E. Härtter, Ein Beitrag zur Theorie der Minimalbasen, J. Reine Angew. Math. 196(1956), 170–204.MathSciNetzbMATHGoogle Scholar
  9. 9.
    J. Hennefeld, Asymptotic nonbases not contained in maximal asymptotic nonbases, preprint.Google Scholar
  10. 10.
    M. B. Nathanson, Minimal bases and maximal nonbases in additive number theory, J. Number Theory 6(1974), 324–333.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. B. Nathanson, s-maximal nonbases of density zero, J. London Math. Soc. 15(1977), 29–34.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    A. Stöhr, Gelöste und ungelöste Fragen über Basen der näturlichen Zahlenreihe, J. Reine Angew. Math. 194(1955), 40–65, 111–140.MathSciNetzbMATHGoogle Scholar
  13. 13.
    S. Turjányi, On maximal asymptotic nonbases of density zero, J. Number Theory 9(1977), 271–275.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Melvyn B. Nathanson
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

Personalised recommendations