Ponderable 3.1.2

Let’s write it:

$\prod _{1⩽i<j⩽n}\frac{\mathrm{fg}\left(i\right)-\mathrm{fg}\left(j\right)}{i-j}=\prod _{1⩽i<j⩽n}\frac{g\left(i\right)-g\left(j\right)}{i-j}\prod _{1⩽i<j⩽n}\frac{\mathrm{fg}\left(i\right)-\mathrm{fg}\left(j\right)}{g\left(i\right)-g\left(j\right)}$ or g is a bijection, so we can reorganize i and j such as the last product is $\prod _{1⩽i<j⩽n}\frac{f\left(i\right)-f\left(j\right)}{i-j}$.

Therefore, sign(fg)=sign(f)sign(g).

Maison