Re: numtoperm abd Factorial Number System

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sat, Oct 06, 2012 at 07:56:13PM -0400, Mathieu Carbou wrote:
> I was wondering why in PARI the numtoperm does not match the Nth
> permutation in the factorial number system ?
> 
> Is there a way to use numtoperm to get the good result or I have to code
> a function which decompose the number in the factorial number system by
> myself ?

You can use this 

mynumtoperm(n,a)=Vec(Vecsmall(numtoperm(n,a))^-1*vectorsmall(n,i,n+1-i))
mypermtonum(p)=permtonum(Vec(vectorsmall(#p,i,#p+1-i)*Vecsmall(p)^-1))

? for(i=0,5,print(mynumtoperm(3,i)))
[1,2,3]
[1,3,2]
[2,1,3]
[2,3,1]
[3,1,2]
[3,2,1]

Cheers,
Bill.