Skip to main content
SpringerLink
Log in

Fractal digital sums and codes

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

The positivity of a special digital sum is proved and its fractal nature is discussed. The result is interpreted in terms of running digital sums of a special code.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Coquet, J.: A Summation Formula Related to the Binary Digits, Invent. Math. 73, 107–115 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  2. Drmota, M., Skalba, M.: Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series, Manuscripta Math. 86, 519–541 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Flajolet, P., Grabner, P. J., Kirschenhofer, P., Prodinger, H., Tichy, R. F.: Mellin transforms and asymptotics: digital sums. Theoret. Comput. Sci. 123, 291–314 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Flajolet, P., Ramshaw, L.: A note on Gray code and odd-even merge, SIAM J. Comput. 9, 142–158 (1980)

    MATH  MathSciNet  Google Scholar 

  5. Flajolet, P., Raoult, J. C., Vuillemin, J.: The number of registers required for evaluating arithmetic expressions. Théoret. Comput. Sci. 9, 99–125 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  6. Goldstein, S., Kelly, K. A., Speer, E. R.: The fractal structure of rarefied sums of the Thue-Morse sequence. J. Number Th. 42, 1–19 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Grabner, P. J.: Completely q-Multiplicative Functions: the Mellin Transform Approach, Acta Arith. 65, 85–96 (1993)

    MATH  MathSciNet  Google Scholar 

  8. Grabner, P. J.: A Note on the Parity of the Sum-of-Digits Function. Actes 30e Séminaire Lotharingien, pp. 35–42, 1993

  9. Litsyn, S., Tietäväinen, A.: Character Sum Constructions of Constrained Error-Correcting Codes, Appl. Algebra Eng., Comp. 5, 45–51 (1994)

    Article  MATH  Google Scholar 

  10. Newman, D. J.: On the number of binary digits in a multiple of three. Bull. Am. Math. Soc. 21, 719–721 (1969)

    MATH  Google Scholar 

  11. Schouhamer-Immink, K. A.: Coding Techniques for Digital Recorders. Englewood Cliffs: Prentice-Hall 1991

    Google Scholar 

  12. IEEE Trans. Inform. Theory, Special Issue on Coding for Storage Devices, Part 2 (May 1991)

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Graz Steyrergasse 30, A-8010, Graz, Austria

    Peter J. Grabner & Robert F. Tichy

  2. Department of Mathematics, Kossuth Lajos University, Egyetem tér 1, 4010, Debrecen, Hungary

    Tamás Herendi

Authors
  1. Peter J. Grabner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tamás Herendi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert F. Tichy
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

These authors were supported by the Austrian National Bank, project Nr. 4995

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grabner, P.J., Herendi, T. & Tichy, R.F. Fractal digital sums and codes. AAECC 8, 33–39 (1997). https://doi.org/10.1007/s002000050050

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002000050050

Keywords

Search

Navigation