Skip to main content
SpringerLink
Log in

Estimating the number of good permutations by a modified fast simulation method

  • Systems Analysis
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

A permutation (s0, s1,…, sN − 1) of symbols 0, 1,…, N − 1 s called good if the set (t0, t1,…, tN − 1) formed according to the rule ti = i + si (mod N), i = 0, 1,…, N − 1, is a permutation too. A modified fast simulation method is proposed to evaluate the number of good permutations for N = 205 with a 5% relative error. Empirical upper and lower bounds for the number of good permutations are also given.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. N. Sachkov, Introduction to Combinatorial Methods of Discrete Mathematics [in Russian], Nauka, Moscow (1982).

    MATH  Google Scholar 

  2. V. N. Sachkov, “Markov chains of iterative conversion systems,” Tr. Diskret. Matem., 6, 165–183 (2002).

    Google Scholar 

  3. J. Hsiang, D. F. Hsu, and Y.-P. Shieh, “On the hardness of counting problems of complete mappings,” Discrete Math., 277, 87–100 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  4. D. F. Hsu and A. D. Keedwell, “Generalized complete mappings, neofields, sequenceable groups and block designs. II,” Pacific J. Math., 117, 291–312 (1985).

    MATH  MathSciNet  Google Scholar 

  5. C. Cooper, R. Gilchrist, I. N. Kovalenko, and D. Novakovic, “Estimation of the number of “good” permutations with application to cryptography,” Cybern. Syst. Analysis, 35, No. 5, 688–693 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Konheim, Cryptography: A Primer, Wiley, Chichester (1991).

    Google Scholar 

  7. Y.-P. Shieh, “Partition strategies for #P-complete problem with applications to enumerative combinatorics,” Ph.D. Thesis, Nat. Taiwan Univ. (2001).

  8. http://www.research.att.com/~njas/sequences/A003111.

  9. C. Cooper and I. N. Kovalenko, “An upper bound for the number of complete mappings,” Teor. Veroyatn. Mat. Statistika, 53, 69–75 (1995).

    MATH  Google Scholar 

  10. I. N. Kovalenko, “Upper bound on the number of complete maps,” Cybern. Syst. Analysis, 32, No. 1, 65–68 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  11. A. A. Levitskaya, “A combinatorial problem in a class of permutations over a ring Z n of residues odd modulo n,” Probl. Upravl. Inform., No. 5, 99–108 (1996).

  12. N. Yu. Kuznetsov, “Applying fast simulation to find the number of good permutations,” Cybern. Syst. Analysis, 43, No. 6, 830–837 (2007).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    N. Yu. Kuznetsov

Authors
  1. N. Yu. Kuznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 101–109, July–August 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuznetsov, N.Y. Estimating the number of good permutations by a modified fast simulation method. Cybern Syst Anal 44, 547–554 (2008). https://doi.org/10.1007/s10559-008-9025-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-008-9025-9

Keywords

Search

Navigation