Consider the two sets $L=\{a,b,c\}$ and $I=\{1,2,3\}$. There are six possible ways to pair up elements of the two sets:
1: $a\to1$, $b\to2$, $c\to3$
2: $a\to1$, $b\to3$, $c\to2$
3: $a\to2$, $b\to1$, $c\to3$
4: $a\to2$, $b\to3$, $c\to1$
5: $a\to3$, $b\to1$, $c\to2$
6: $a\to3$, $b\to2$, $c\to1$
Question: I want a compact way to refer to each of the 6 objects above that describes how the elements of $L$ are mapped to the elements of $I$. What is the proper (standard) notation to represent the labelings?
What comes into mind is permutations. While this is not strictly permutations the same notation might be used. For example the first being $\begin{pmatrix}a & b & c \\ 1 & 2 & 3\end{pmatrix}$. Note however that the notation might be confused with a normal matrix (as it also can for permutations) so it would be wise to define the notation if used.