Definition:Sign of Permutation

Definition
Let $S_n$ denote the symmetric group on $n$ letters.

Also denoted as
In physics and applied mathematics, the symbol $e_{ijk}$ can often be found for this concept, referred to as the alternating symbol, defined as:
 * $e_{ijk} = \begin{cases}

1 & : \text{if $\left({i, j, k}\right)$ is an even permutation of $\left({1, 2, 3}\right)$} \\ -1 & : \text{if $\left({i, j, k}\right)$ is an odd permutation of $\left({1, 2, 3}\right)$}\\ 0 & : \text{if any two of $\left\{{i, j, k}\right\}$ are equal}\end{cases}$

Also known as
The sign of a permutation is also known as its signum.

However, on this is not recommended, in order to keep this concept separate from the signum function on a set of numbers.

Also see

 * Equivalence of Definitions of Sign of Permutation