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-rw-r--r--mgr.tex14
-rw-r--r--subtree-with-hole.pdfbin0 -> 9260 bytes
-rw-r--r--subtree-with-hole.pdf_tex58
3 files changed, 72 insertions, 0 deletions
diff --git a/mgr.tex b/mgr.tex
index f7c66fd..ec250b6 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -1059,6 +1059,20 @@ components:
doesn't lie on the $w$ to $v$ path.
\end{itemize}
+\begin{figure}
+ \centering
+ \def\svgwidth{0.5\columnwidth}
+ \input{subtree-with-hole.pdf_tex}
+ \caption{
+ The subtree of $v$ with hole $w$. All its nodes can be partitioned into
+ the path $u_1, \ldots, u_4 = v$ and the subtrees of $u_1', \ldots,
+ u_4'$.
+ }\label{subtree-with-hole-figure}
+\end{figure}
+
+Figure \ref{subtree-with-hole-figure} depicts a subtree with hole labeled
+according to this nomenclature.
+
With our bottom-up computation, we've already computed the new state in $w$.
There have been no relabelings in the subtrees of the $u_i'$'s, so we can get
their states from the precomputed run of $A$ on the original tree. Now consider
diff --git a/subtree-with-hole.pdf b/subtree-with-hole.pdf
new file mode 100644
index 0000000..50f5404
--- /dev/null
+++ b/subtree-with-hole.pdf
Binary files differ
diff --git a/subtree-with-hole.pdf_tex b/subtree-with-hole.pdf_tex
new file mode 100644
index 0000000..ae74b70
--- /dev/null
+++ b/subtree-with-hole.pdf_tex
@@ -0,0 +1,58 @@
+%% Creator: Inkscape 1.1.1 (3bf5ae0d25, 2021-09-20, custom), www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'subtree-with-hole.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%% \input{<filename>.pdf_tex}
+%% instead of
+%% \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%% \def\svgwidth{<desired width>}
+%% \input{<filename>.pdf_tex}
+%% instead of
+%% \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%% \usepackage{import}
+%% in the preamble, and then including the image with
+%% \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%% \graphicspath{{<path to file>/}}
+%%
+%% For more information, please see info/svg-inkscape on CTAN:
+%% http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+ \makeatletter%
+ \providecommand\color[2][]{%
+ \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+ \renewcommand\color[2][]{}%
+ }%
+ \providecommand\transparent[1]{%
+ \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+ \renewcommand\transparent[1]{}%
+ }%
+ \providecommand\rotatebox[2]{#2}%
+ \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+ \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+ \ifx\svgwidth\undefined%
+ \setlength{\unitlength}{734.22219354bp}%
+ \ifx\svgscale\undefined%
+ \relax%
+ \else%
+ \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+ \fi%
+ \else%
+ \setlength{\unitlength}{\svgwidth}%
+ \fi%
+ \global\let\svgwidth\undefined%
+ \global\let\svgscale\undefined%
+ \makeatother%
+ \begin{picture}(1,0.9804307)%
+ \lineheight{1}%
+ \setlength\tabcolsep{0pt}%
+ \put(0,0){\includegraphics[width=\unitlength,page=1]{subtree-with-hole.pdf}}%
+ \end{picture}%
+\endgroup%