Random feedback shift registers and the limit distribution for largest cycle lengths

For a random binary noncoalescing feedback shift register of width n , with all 2^2ⁿ⁻¹ possible feedback functions f equally likely, the process of long cycle lengths, scaled by dividing by N=2ⁿ , converges in distribution to the same Poisson–Dirichlet limit as holds for random permutations in SN , with all $N!$ possible permutations equally likely. Such behaviour was conjectured by Golomb, Welch and Goldstein in 1959.