Maple: Generating a set of permutations.
I want to create all permutations of the following expression.
$a_1 a_2 a_3 ..a_n a_n'.. a_3' a_2' a_1'$
Where a variable can only be swapped with it's prime partner.
Since there are n variables each with 2 possible positions I can see that there must be $2^n$ permutations.
I've not used Maple for 5 years so the more detailed the answer the better.
Ideally I would like the output to be a vector as I'm going to be creating a matrix by combining the output of this vector with another vector.
Any help greatly appreciated. Thanks, Ben
$\endgroup$1 Answer
$\begingroup$Here is a code fragment to help you get started:
P := proc(n) local res, ind, d, perm; res := []; for ind from 2^n to 2*2^n-1 do d := convert(ind, base, 2)[1..n]; perm := [seq(`if`(d[p]=0, a[p], b[p]), p=1..n), seq(`if`(d[n+1-p]=0, b[n+1-p], a[n+1-p]), p=1..n)]; res := [op(res), perm]; od; res; end;
Sample run is
> P(4); [[a[1], a[2], a[3], a[4], b[4], b[3], b[2], b[1]], [b[1], a[2], a[3], a[4], b[4], b[3], b[2], a[1]], [a[1], b[2], a[3], a[4], b[4], b[3], a[2], b[1]], [b[1], b[2], a[3], a[4], b[4], b[3], a[2], a[1]], [a[1], a[2], b[3], a[4], b[4], a[3], b[2], b[1]], [b[1], a[2], b[3], a[4], b[4], a[3], b[2], a[1]], [a[1], b[2], b[3], a[4], b[4], a[3], a[2], b[1]], [b[1], b[2], b[3], a[4], b[4], a[3], a[2], a[1]], [a[1], a[2], a[3], b[4], a[4], b[3], b[2], b[1]], [b[1], a[2], a[3], b[4], a[4], b[3], b[2], a[1]], [a[1], b[2], a[3], b[4], a[4], b[3], a[2], b[1]], [b[1], b[2], a[3], b[4], a[4], b[3], a[2], a[1]], [a[1], a[2], b[3], b[4], a[4], a[3], b[2], b[1]], [b[1], a[2], b[3], b[4], a[4], a[3], b[2], a[1]], [a[1], b[2], b[3], b[4], a[4], a[3], a[2], b[1]], [b[1], b[2], b[3], b[4], a[4], a[3], a[2], a[1]]]$\endgroup$ 3
