From 2ea016d15ca9f777fc99e9f6b2b5a144b056da23 Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Thu, 9 Dec 2021 15:39:00 +0100
Subject: Specify rooted trees

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 mgr.tex | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

(limited to 'mgr.tex')

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
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