] >
Let’s write it:
∏ 1 ⩽ i < j ⩽ n fg i − fg j i − j = ∏ 1 ⩽ i < j ⩽ n g i − g j i − j ∏ 1 ⩽ i < j ⩽ n fg i − fg j g i − g j or g is a bijection, so we can reorganize i and j such as the last product is ∏ 1 ⩽ i < j ⩽ n f i − f j i − j .
Therefore, sign(fg)=sign(f)sign(g).
Maison