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 ^^;
It will be ticket #12872.
Nathann
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