Is there a name or symbol convention for what I might call the "anti" Kronecker delta (that is, $1 - \delta_{ij}$)?
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$\begingroup$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.
$\endgroup$ $\begingroup$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, $[i \not= j]$.
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