\begin{xpl}
-Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=3$), and that
+Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=2$), and that
$s=\left\{
\begin{array}{l}
u=\underline{6,} ~ \underline{11,5}, ...\\
The \textsc{Figure~\ref{graphe1}} shows what happens when
displaying each iteration result.
On the contrary, the \textsc{Figure~\ref{graphe2}} explicits the behaviors
-when always applying 2 or 3 modification and next outputing results.
+when always applying either 2 or 3 modifications before generating results.
Notice that here, orientations of arcs are not necessary
since the function $f_0$ is equal to its inverse $f_0^{-1}$.
\end{xpl}
In this context, $\mathcal{P}$ is the singleton $\{b\}$.
If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach
its neighborhood and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
- If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself
+ If $b$ is odd, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself
and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
\end{proof}
-The next section shows how to generate functions and a iteration number $b$
+The next section recalls a general scheme to produce
+functions and a iteration number $b$
such that $\Gamma_{\{b\}}$ is strongly connected.
-
\ No newline at end of file
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
