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1 files changed, 5 insertions, 5 deletions
diff --git a/mgr.tex b/mgr.tex
index dfbb56d..8ecbc83 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -223,8 +223,8 @@ The rest of our work is organized in the following way:
We work with finite rooted trees whose vertices are labeled with letters from a
finite alphabet. More formally, given a finite alphabet $\Sigma$, for each $a
-\in \Sigma$, $a$ is a tree, and if $t_1, \ldots, t_k$ are trees, then $a(t_1,
-\ldots, t_k)$ is also a tree. A tree $T$ can then also be seen as an acyclic
+\in \Sigma$, $a$ is a tree, and if $T_1, \ldots, T_k$ are trees, then $a(T_1,
+\ldots, T_k)$ is also a tree. A tree $T$ can then also be seen as an acyclic
undirected graph with vertex set $V(T)$ and edge set $E(T)$, with a
distinguished root vertex $r \in V(T)$.
@@ -240,7 +240,7 @@ Take a binary tree $T$. The \definedterm{post-order} of $V(T)$ is an ordering of
$T$'s vertices produced by the following recursive procedure:
\begin{enumerate}
- \item First traverse the root's children's subtrees.
+ \item Traverse the root's children's subtrees.
\item Visit the root.
\end{enumerate}
@@ -248,14 +248,14 @@ Similarly, the \definedterm{pre-order} of $V(T)$ is produced by the following
recursive procedure:
\begin{enumerate}
- \item First visit the root.
+ \item Visit the root.
\item Traverse the root's children's subtrees.
\end{enumerate}
Finally, the following procedure produces the \definedterm{in-order} of $V(T)$:
\begin{enumerate}
- \item First traverse the left child's subtree.
+ \item Traverse the left child's subtree.
\item Visit the root.
\item Traverse the right child's subtree.
\end{enumerate}