\begin{definition}[Definition:Permutation on n Letters/Two-Row Notation]
Let $\pi$ be a permutation on $n$ letters.
The '''two-row notation''' for $\pi$ is written as two rows of elements of $\N_n$, as follows:
:$\pi = \begin{pmatrix}
1 & 2 & 3 & \ldots & n \\
\map \pi 1 & \map \pi 2 & \map \pi 3 & \ldots & \map \pi n
\end{pmatrix}$
The bottom row contains the effect of $\pi$ on the corresponding entries in the top row.
\end{definition}