Permutation/Sign/Product of differences/Definition

Sign

Let ${}M=\{1,\ldots ,n\}$ and let ${}\pi$ be a permutation on ${}M$. Then we call the number

${}\operatorname {sgn} (\pi )=\prod _{i<j}{\frac {\pi (j)-\pi (i)}{j-i}}\,$

the sign of the permutation ${}\pi$.