Random Permutations of a Given Length

ρ

0.

number of samples

200

new random case

77777

Generate random permutations on

n

letters that have a "length" within a fixed range. The space of all permutations on

n

letters is stratified by the degree to which a given permutation mixes up the

n

letters. This Demonstration shows how to generate permutations of a given length using essentially Gaussian copula. The parameter

ρ

determines the degree of disorder, with

ρ=0

being total disorder,

ρ=1

signifying no disorder, and

ρ=-1

indicating reversal of order. The red dots are a graph of the points

(i,π(i))

for the given permutation chosen. The gold line is the permutation length scaled by the number of samples. You can change the number of samples or look at many samples with similar permutation lengths by changing the new random case slider. Notice that scrolling through new cases with a given

ρ

produces almost no variation in permutation length though many different permutations.