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Cybernetics and Systems Analysis

, Volume 43, Issue 6, pp 830–837 | Cite as

Applying fast simulation to find the number of good permutations

  • N. Yu. Kuznetsov
Article

Abstract

A permutation (s0, s1,…, sN − 1) of symbols 0, 1,…, N − 1, is 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 also a permutation. A fast simulation method is proposed. It allows the number of good permutations to be evaluated with high accuracy for large N (in particular, N > 100). Empirical upper and lower bounds for the number of good permutations are presented and verified against numerical data.

Keywords

permutation fast simulation method unbiased estimate sample variance relative error 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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