What does $\left \lbrace r, l,0 \right \rbrace ^{\mathbb{Z}^2}$ mean?

Question

What is the meaning of this notation? $$ \left\{a, b\right\}^{[c, d]} $$

Answer 1

The notation $A^B$ usually means the set of all functions $B \to A$.

Answer 2

The notation $A^B$ for sets $A$ and $B$ typically means the set of all function from $B$ to $A$.

Answer 3

$A^B$ in general means the set of functions from $B$ to $A$. The notation is reasonable since for example $\mathbb{R}^2$, which is pairs of real numbers, can be considered as the set of functions from $\{1,2\}$, which is a set of size $2$, to the real numbers --- the image of $1$ gives the first coordinate and the image of $2$ the second.