The Levi-Civita tensor is the fully anti-symmetric tensor with

(Subscript[ϵ, i, j, k])  = 0, if two or more indices are equal

\(TraditionalForm\`ϵ\_\(1, 2, 3\)\ \  = \ \(ϵ\_\(2, 3, 1\)\ \  = \ \(ϵ\_\(3, 1, 2\)\ \  = \ 1\)\)\ \)
\(TraditionalForm\`ϵ\_\(3, 2, 1\)\ \  = \ \(ϵ\_\(2, 1, 3\)\ \  = \ \(ϵ\_\(1, 3, 2\)\ \  = \(-1\)\)\)\)