Using the Monte Carlo Method for Fast Simulation of the Number of “Good” Permutations on the SCIT-4 Multiprocessor Computer Complex

A permutation ( s 0 , s 1, ⋯, s N − 1 ) of symbols 0,1, ,⋯ , N − 1 is called “good” if the set ( t 0 , t 1,⋯, t N − 1 ) formed by the rule t i= i + s i (mod N ), i = 0,1,⋯, N − 1, is also a permutation. The author proposes the fast simulation method. Its implementation on the SCIT-4 multiprocessor computer complex makes it possible to evaluate the number of “good” permutations for N ≤ 305 with relative accuracy no greater than 1%. The number of “good” permutations is estimated for N 25, 35, ⋯, 305 .