In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers 1, 2, ..., n, for some positive integer n.

What is the permutation symbol?

The permutation symbol, sometimes called the Levi-Civita symbol, can have any number of subscripts. If any two of the subscripts are equal, the symbol evaluates to 0. Otherwise, the symbol evaluates to 1 or -1. If you can order the indices with an even number of swaps, the sign of the permutation is 1.

How do you write a permutation?

When writing permutations, we use the notation nPr, where n represents the number of items to choose from, P stands for permutation and r stands for how many items you are choosing. To calculate the permutation using this formula, you would use nPr = n! / (n - r)!.