comment out no. of walks

blueprint/src/content.tex

@@ -627,13 +627,13 @@ \chapter{Nondeterminism and overlap-free words}\label{chap:EJC}
 			\sum_{i=0}^{t} \ell_i = 2m-1 - 2t
 			\]
 			which is impossible.
-			The number of walks is
-			\begin{align*}
-		   W_{m,2m+1}&=& \sum_{t=0}^{m-1}\sum_{\makecell{\{\ell_0,\dots,\ell_t\ge 0:\\ \sum\ell_i = 2m-1-2t\}}}\prod_{i=0}^t W_{m-1,\ell_i}\\
-		   &=& \sum_{\makecell{\{\ell_0\ge 0:\\ \ell_0 = 2m-1\}}}W_{m-1,\ell_0}\\
-			&=&W_{m-1,2m-1} \\
-			&=&1&&(\text{ind.~hyp.})
-			\end{align*}
+			% The number of walks is
+			% \begin{align*}
+			% 		   W_{m,2m+1}&=& \sum_{t=0}^{m-1}\sum_{\makecell{\{\ell_0,\dots,\ell_t\ge 0:\\ \sum\ell_i = 2m-1-2t\}}}\prod_{i=0}^t W_{m-1,\ell_i}\\
+			% 		   &=& \sum_{\makecell{\{\ell_0\ge 0:\\ \ell_0 = 2m-1\}}}W_{m-1,\ell_0}\\
+			% &=&W_{m-1,2m-1} \\
+			% &=&1&&(\text{ind.~hyp.})
+			% \end{align*}
 
 			If $n>0$ is even then $x=ya$ where $\abs{y}$ is odd; by the second subword inequality \Cref{subword} \Cref{AN case}, $A_N(x)\le A_N(y)+1$, as desired.
 			Finally, if $n=0$ then the result follows from $A_N(\eps)=1$.