Permutations to scalars and back again.

[Georgi Guninski]

On Mon, Sep 12, 2016 at 07:50:50PM +1000, James A. Donald wrote:
> To restate the problem:  Find a mapping between integers and injective
> functions from N to X up to a permutation of N.
> 
> In this case, find a mapping between integers and an injective functions
> from 18 to 36.

Sage (open source, sagemath.org) can do at least parts of what you
are asking.
Not sure I get the question about injective function, but AFAICT
treating the permutation as nonnegative integer in binary will do.

Example sage session:

sage: l=[0]*2+[1]*2
sage: pe=Permutations(l)
sage: pe.cardinality()
6
sage: pe[0]
[0, 0, 1, 1]
sage: for p in pe:  print p
[0, 0, 1, 1]
#...more