name or symbol for "anti" Kronecker delta?

Question

Is there a name or symbol convention for what I might call the "anti" Kronecker delta (that is, $1 - \delta_{ij}$)?

Answer 1

I don't think there is an agreed upon notation for this. However, you could just define $\gamma_{ij}=1-\delta_{ij}$ if you need to.

Answer 2

You could use the Inverson bracket. If $P$ is a property, then $$ [P] = \begin{cases} 1 &\text{if $P$ is true}\\ 0 &\text{otherwise} \end{cases} $$ Thus, in your case, $[i \not= j]$.