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\citation{BollobasRiordan}
\citation{BollobasRiordan}
\@writefile{toc}{\contentsline {section}{\numberline {1}Review}{1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Portions of the lattice $L = \mathbb  {Z}^2$ (solid lines) and the isomorphic dual lattice $L^*$}}{2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Four rectangles forming a square annulus}}{2}}
\newlabel{fig:Annulus}{{2}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Proof of Harris' Theorem}{2}}
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\bibcite{BollobasRiordan}{1}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces A rectangle $R$ and square $S$ inside it, drawn with paths (solid curves) whose presence as open paths would imply $X(R)$}}{5}}
\newlabel{fig:X(R)}{{3}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The overlapping rectangles $R$ and $R'$ with the square $S$ in their intersection. The paths drawn show that $X(R)$ holds, as well as the reflected equivalent for $R'$. If $H(S)$ also holds, then so does $H(R \DOTSB \bigcup@ \slimits@ R')$}}{5}}
\newlabel{fig:last}{{4}{5}}