\begin{figure}[tb]
\centering
\begin{subfigure}{0.15\linewidth} \centering
\begin{tikzpicture}[x=0.45cm,y=0.45cm,scale=0.8]
\begin{scope}[gray, thin]
\draw (-1,0)--(-1,4);
\draw (0,0)--(0,4);
\draw (1,0)--(1,4);
\draw (2,1)--(2,4);
\draw (3,2)--(3,4);
\draw (4,3)--(4,4);
\draw(-1.5,0)--(1,0);
\draw(-1.5,1)--(2,1);
\draw(-1.5,2)--(3,2);
\draw(-1.5,3)--(4,3);
\draw(-1.5,4)--(5,4);
%\draw (1,2)--(1,5);
%\draw (-6.5,1) grid[step=0.7cm] (3.5,5);
\end{scope}
\filldraw
(3,4) circle[radius=2pt]
(2,3) circle[radius=2pt]
(1,2) circle[radius=2pt]
(0,1) circle[radius=2pt]
(0,0) circle[radius=2pt];
\draw[very thick] (0,0)--(1,0)--(1,1)--(2,1)--(2,2)--(3,2)--(3,4);
\draw[very thick] (0,0)[xshift=3pt,yshift=3pt]--(0,0)[xshift=-6pt]--(1,0)--(1,1)[xshift=6pt]--(1,1)[yshift=-3pt]--(1,3)[xshift=-3pt]--(2,3);
\draw[very thick] (0,0)[xshift=3pt,yshift=3pt]--(0,0)[yshift=-3pt]--(0,2)--(1,2);
\draw[very thick] (0,0)--(0,1);
\end{tikzpicture}
\caption{}
\label{fig:oopathsshift}
\end{subfigure}
\begin{subfigure}{0.22\linewidth} \centering
\begin{tikzpicture}[x=0.45cm,y=0.45cm,yscale=0.7,xscale=0.4]
\begin{scope}[fill=red!25,semithick]
\filldraw (-1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(2,2)--++(1,-1)--++(-2,-2)--++(-2,0)--++(-1,-1)--++(-2,0)--++(-1,-1)--++(-2,0)--cycle;
\filldraw (-2,2)--++(2,0)--++(3,3)--++(2,0)--++(1,-1)--++(-2,0)--++(-3,-3)--++(-2,0)--cycle;
\filldraw (-2,2)--++(2,2)--++(2,0)--++(-1,1)--++(-2,0)--++(-2,-2)--cycle;
\filldraw (-4,4)--(-3,5)--(-2,4)--(-3,3)--cycle;
\end{scope}
\begin{scope}[very thin]
\draw(2,0)--(0,2) (3,1)--(1,3)--(-1,3)--(-2,4) (5,1)--(4,2) (6,2)--(5,3)--(3,3)--(2,4)--(0,4)--(-1,5) (8,2)--(7,3) (9,3)--(8,4)--(6,4)--(5,3) (4,4)--(3,5);

\end{scope}
\draw[thick] (0,0)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(-4,0)--++(-1,1)--++(-2,0)--++(-1,-1)--++(-1,1)--++(-2,0)--++(-1,-1)--++(-1,1)--++(-2,0)--++(-1,-1)--++(-1,1)--++(-1,-1)--++(-1,1)--cycle;
\end{tikzpicture}
\caption{}
\label{fig:oopathstiling}
\end{subfigure}%
\begin{subfigure}{0.22\linewidth} \centering
\begin{tikzpicture}[x=0.45cm,y=0.45cm,yscale=0.7,xscale=0.4]
\draw (-1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(2,2)--++(1,-1)--++(-2,-2)--++(-2,0)--++(-1,-1)--++(-2,0)--++(-1,-1)--++(-2,0)--cycle;
\draw (-2,2)--++(2,0)--++(3,3)--++(2,0)--++(1,-1)--++(-2,0)--++(-3,-3)--++(-2,0)--cycle;
\draw (-2,2)--++(2,2)--++(2,0)--++(-1,1)--++(-2,0)--++(-2,-2)--cycle;
\draw (-4,4)--(-3,5)--(-2,4)--(-3,3)--cycle;
\draw(2,0)--(0,2) (3,1)--(1,3)--(-1,3)--(-2,4) (5,1)--(4,2) (6,2)--(5,3)--(3,3)--(2,4)--(0,4)--(-1,5) (8,2)--(7,3) (9,3)--(8,4)--(6,4)--(5,3) (4,4)--(3,5) (6,4)--(7,5);
\draw (11,5)--(10,4)--(12,4)--(13,5);
\begin{scope}[ultra thick]
\draw[red] (-0.5,0.5)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(3,3);
\draw[red] (-1.5,1.5)--++(2,0)--++(3,3)--++(2,0)--++(1,1);
\draw[red] (-2.5,2.5)--++(2,2)--++(2,0)--++(1,1);
\draw[red] (-3.5,3.5)--++(2,2);
\draw[red] (-4.5,4.5)--++(1,1);

\draw[blue] (-4.5,5.5)--++(3,-3)--++(2,0)--++(2,-2);
\draw[blue] (-2.5,5.5)--++(2,-2)--++(2,0)--++(1,-1)--++(2,0)--++(1,-1);
\draw[blue] (1.5,5.5)--++(2,-2)--++(4,0)--++(1,-1);
\draw[blue] (5.5,5.5)--++(1,-1)--++(2,0)--++(1,-1)--++(2,0);
\draw[blue] (9.5,5.5)--++(1,-1)--++(4,0);

\draw[green!80!black] (1,0)--++(-2,2)--++(2,2)--++(-1,1);
\draw[green!80!black] (4,1)--++(-1,1)--++(2,2)--++(-1,1);
\draw[green!80!black] (7,2)--++(-1,1)--++(2,2);
\draw[green!80!black] (10,3)--++(2,2);
\draw[green!80!black] (13,4)--++(1,1);
\end{scope}
\draw[thick] (0,0)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(2,0)--++(1,1)--++(-4,0)--++(-1,1)--++(-1,-1)--++(-2,0)--++(-1,1)--++(-1,-1)--++(-2,0)--++(-1,1)--++(-1,-1)--++(-2,0)--++(-1,1)--++(-1,-1)--++(-1,1)--++(-1,-1)--cycle;
\end{tikzpicture}
\caption{}
\label{fig:oopathsrgb}
\end{subfigure}%
\begin{subfigure}{0.22\linewidth} \centering
\begin{tikzpicture}[x=0.45cm,y=0.45cm,scale=0.8]]
\draw[red,thick](-2,5)--(-3,6);
\draw[red,thick](0,5)--(-1,6);
\draw[red,thick](1,2)--(0,3);
\draw[red,thick](2,3)--(1,4);
\draw[red,thick](0,1)--(-1,2);
\draw[red,thick](-1,2)--(-2,3);
\fill[cyan!70] (4,5) rectangle (2,6) rectangle (3,4) (0,6) rectangle (1,4) rectangle (-1,5) rectangle (0,3) (-3,5) rectangle (-2,3);
%\begin{scope}[fill=yellow!95!black]
%\fill (0,1) rectangle node {1} ++(-1,1)
%rectangle node {3} ++(-1,1);
%\fill (-2,5) rectangle node {7} ++(-1,1);
%\fill (0,5) rectangle node {5} ++(-1,1);
%\fill (0,2) rectangle node {1} ++(1,1) rectangle node {1} ++(1,1);
%\end{scope}
\begin{scope}[very thin]
\draw(-5,5)--(-5,6);
\draw(-4,4)--(-4,6);
\draw(-3,3)--(-3,6);
\draw(-2,2)--(-2,6);
\draw(-1,1)--(-1,6);
\draw(0,1)--(0,6);
\draw (1,2)--(1,6);
\draw (2,3)--(2,6);
\draw (3,4)--(3,6);
\draw(-1,1)--(0,1);
\draw(-2,2)--(1,2);
\draw(-3,3)--(2,3);
\draw(-4,4)--(3,4);
\draw(-5,5)--(4,5);
\draw(-5,6)--(4,6);
\end{scope}
\draw[very thick] (-1,1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)
--++(-2,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(-1,0)--cycle;
\end{tikzpicture}
\caption{}
\label{fig:oorevexcite}
\end{subfigure}
\begin{subfigure}{0.15\linewidth}
\ytableausetup{smalltableaux}
\ytableaushort{
\none\none\none11,\none\none12,\none22,23,3}
\caption{}
\label{fig:ooskewtab}
\end{subfigure}
\caption{Constructions related to the bijection described in \cref{sec:posterms}.}
\label{fig:oopaths}
\end{figure}
