Personal reference on functions whose values depend on the relation between indexes. “Index relation functions” is not a term in actual use by anyone else, but there does not seem to be a word in widespread use for functions like these, where the function values relate indexes against each other.
Kronecker delta
\[ \delta_{ij} = \begin{cases} 1 & \text { for } i = j \\ 0 & \text { for } i \neq j \end{cases} \]
Levi-Civita symbol
\[ \epsilon_{1 2 \ldots n} = 1 \] \[ \epsilon_{\ldots i_p \ldots i_q \ldots} = -\epsilon_{\ldots i_q \ldots i_p \ldots} \]
\[ \epsilon_{ijk} = \begin{cases} 0 & \text { for } i=j \vee j=k \vee k=i \\ 1 & \text { for } (i,j,k) \in \{ (1,2,3), (2,3,1), (3,1,2) \} \\ -1 & \text { for } (i,j,k) \in \{ (3,2,1), (2,1,3), (1,3,2) \} \end{cases} \]