Specify rooted trees

1 files changed, 6 insertions, 5 deletions

diff --git a/mgr.tex b/mgr.tex
index f4bbb74..8b626dc 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -202,13 +202,14 @@ The rest of our work is organized in the following way:
 \section{Definitions}
 \subsection{Trees}
 
-We work with finite 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,
+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
-undirected graph with vertex set $V(T)$ and edge set $E(T)$.
+undirected graph with vertex set $V(T)$ and edge set $E(T)$, with a
+distinguished root vertex $r \in V(T)$.
 
-We use the standard notions of root, child, sibling, ancestor, descendant, etc.
+We use the standard notions of leaf, child, sibling, ancestor, descendant, etc.
 
 Binary trees are trees where each node has either no children (the node is a
 leaf), or exactly two children (which, based on their order, can be called the