What does the notation $ [ i \neq k ] $ mean?
It  is used like a boolean where $[i \neq k] = 1$ if $i \neq k$ and $0$ otherwise. Notice that $[i \neq k]$ is equivalent to $i &lt; k$ or $i &gt; k$ for numbers, which is the right part of the equation you wrote.
It is called Iverson bracket and in general $[statement] = 1$ if $statement$ is true and $0$ otherwise.