On Tue, Apr 24, 2012 at 12:51:34PM +0200, Nathann Cohen wrote:
> Helloooooooo !!
>
> I vote yes. When I teach this, I call this the swapping diagram (not
> standard terminology). The number of swaps gives you the Bruhat
> length, if I remember correctly, when you regard S_n as a Coxeter group.
> The parity gives you the sign of the permutation, which gives you, in
> turn, the
> determinant of the associated matrix. It is a very useful diagram:-)
>
> Hmmm.... I just took a look at it, and it seems I just can not do this for
> my own purposes. I mean, this diagram can be written, but Permutations
> objets basically *cannot* store a permutation between anything different
> from 1 .... n
> Well, it just supposes that the elements in the permutation have some
> "natural linear ordering", which is the one given by the '<' python
> operator. Here is the code from Permutation.inversions :
> p = self[:]
> inversion_list = []
> for i in range(len(p)):
> for j in range(i+1,len(p)):
> if p[i] > p[j]:
> #inversion_list.append((p[i],p[j]))
> inversion_list.append([i,j])
> return inversion_list
> So it looks like I cannot trust it with my strings, for instance :-/
> I will write this diagram anyway. It can prove useful to me later, and it
> looks like you could use it anyway ^^;
You might want to use permutations from the symmetric group instead::
sage: S = SymmetricGroup(10)
sage: x = S.random_element()
sage: x.inversions()
[(2,3), (2,4), (2,5), (4,5), (3,5), (1,5), (2,6), (4,6), (3,6), (1,6),
(5,6), (2,7), (4,7), (3,7), (1,7), (2,8), (4,8)]
It has been implemented recently by Mark, and it will work for any
Coxeter group.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To post to this group, send email to sage-combinat-devel@googlegroups.com.
To unsubscribe from this group, send email to
sage-combinat-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sage-combinat-devel?hl=en.
