Dear forum,
Let G be the symmetric group in n letters. Let s be in G.
I want to compute a "minimal" decomposition of s as a product of the
traspositions:
s_1,...,s_{n-1}, where s_i=(i,i+1).
"Minimal" means: of minimal length.
For instance: if n=7 and s=(2,4,5,3) (6,7), such a decomposition would be
s=(3,4)(2,3)(4,5)(6,7)=s_3 s_2 s_4 s_6.
So, I would like something like this:
???(G,s);
(3,4)(2,3)(4,5)(6,7)
????(G,s);
4 (the length).
How can I do that?
Thank you in advance.
Best, Fernando F.
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