Kronecker delta function notation

Question

Can someone please help me, what does $\delta_{i-j-1}$ stand for? I have a matrix with elements $z_{ij}=\delta_{i-j-1}$ where $\delta_k$ is the Kronecker delta function (that's how it's written in the text). I'm confused with minus sign in the index, I know the definition $\delta_{ik}=1\quad iff\quad i=j,$ 0 otherwise.

Answer 1

From Kronecker delta:Alternative notation:

Often, the notation $\delta_i$ is used. $$ \delta_{k} = \begin{cases} 0, & \mbox{if } k \ne 0 \\ 1, & \mbox{if } k=0 \end{cases} $$

Set $k=i-j-1$...