I have noticed that when I iterate permutations of short vectors with the same
seed, the cycle lengths are much shorter than I would expect by chance. For
example:
X <- 1:10
Xorig <- X
start <- 112358
N <- 10
for (i in 1:N) {
seed <- start + i
for (j in 1:1000) { # Maximum cycle length to consider
set.seed(seed) # Re-seed RNG to same initial state
X <- sample(X) # Permute X and iterate
if (all(X == Xorig)) {
cat(sprintf("Seed:\t%d\tCycle: %d\n", seed, j))
break()
}
}
}
Seed: 112359 Cycle: 14
Seed: 112360 Cycle: 14
Seed: 112361 Cycle: 8
Seed: 112362 Cycle: 14
Seed: 112363 Cycle: 8
Seed: 112364 Cycle: 10
Seed: 112365 Cycle: 10
Seed: 112366 Cycle: 10
Seed: 112367 Cycle: 9
Seed: 112368 Cycle: 12
I understand that I am performing the same permutation operation over and over
again - but I don't see why that would lead to such a short cycle (in fact the
cycle for the first 100,000 seeds is never longer than 30). Does this have a
straightforward explanation?
Thanks!
Boris
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