Definition:Permutation Symbol

It has been suggested that this page or section be merged into Definition:Sign of Permutation. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code.

This article needs to be linked to other articles. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code.

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