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

A permutation (s₀, s₁,…, s_{N − 1}) of symbols 0, 1,…, N − 1 s called good if the set (t₀, t₁,…, t_{N − 1}) formed according to the rule t_i = i + s_i (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. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 101–109, July–August 2008.