For $n \in \mathbb{N}$, and $\sigma \in Sym(n)$ a permutation of $n$ elements, the *Levi-Civita symbol* or *antisymmetric symbol*

$\epsilon_{\sigma(1), \sigma(2), \cdots, \sigma(n)}
\;\in\;
\{\pm 1\}$

is (tensor-style notation for) the signature of the permutation.

Together with the Kronecker delta-notation, the Levi-Civita symbol is convenient in expressions subject to Einstein summation convention, then serving essentially as a combinatorial form of string diagram/Penrose notation in tensor categories.

See also

- Wikipedia,
*Levi-Civita symbol*

Last revised on March 16, 2020 at 17:53:25. See the history of this page for a list of all contributions to it.