Is there an expression for $i, j, k \in \left\{1,\, 2,\, 3\right\}$ with $i \neq j \neq k$?

Question

I want to make a statement where $i, j, k \in \left\{1,2,3\right\}$ but $i \neq j \neq k$ and assumed there'd be an equivalent of $$ \delta_{ij} = \begin{cases} 0, & i = j \\ 1, & i \neq j \end{cases} $$

This led me to wonder if there is some other generalization?

Answer 1

The absolute value of the Levi-Civita symbol $\varepsilon_{ijk}$. https://en.wikipedia.org/wiki/Levi-Civita_symbol

$\varepsilon_{ijk}$ is 1 for (i,j,k) being cyclic permutations of (1,2,3) and -1 for (i,j,k) being cyclic permutations of (1,3,2), and $0$ if there are repetitions.