Definition:Permutation Symbol

Definition
The permutation symbol $\varepsilon$ of a permutation $P$ of a set of elements is defined as:
 * $+1$ for even permutations (permutations that are an even number of pair swaps)
 * $-1$ for odd permutations
 * $0$ if the list of elements is not a permutation (that is, contains a repeated value).

Frequently, the permutation will be explicit, for example:


 * $\varepsilon_{i j k \ldots}$


 * $\varepsilon^{i j \ldots}_{k l \ldots}$


 * $\varepsilon^{i j k \ldots}$

This notation is especially useful when raising and lowering indices (that is, converting between forms and vectors).

Also see

 * Definition:Sign of Permutation