a^{w+2}  \Lhat\left( \begin{tikzpicture}[baseline=.5cm, rounded corners=2mm]
    \draw(-.5,-.5)-- (.5,.5) -- (.1,.9);
    \draw[->] (-.1,1.1)--(-.5,1.5);
    \draw[->] (-.1,.1) -- (-.5,.5)--(.5,1.5);
    \draw (.1,-.1) -- (.5,-.5);
\end{tikzpicture}\right)
+ a^{w} \Lhat\left(
\begin{tikzpicture}[baseline]
    \draw[<-] (1.5,.5) .. controls (2,0) .. (1.5,-.5);
    \draw[<-] (2.5,.5) .. controls (2,0) .. (2.5,-.5);
\end{tikzpicture}\right)
= z
\left( a^{w+1} \Lhat\left( \begin{tikzpicture}[baseline]
    \draw[->] (-.5,-.5)-- (.5,.5);
    \draw[->] (-.1,.1) -- (-.5,.5);
    \draw (.1,-.1) -- (.5,-.5);
\end{tikzpicture}\right)
+ a^{-1} a^{\bullet}
 \Lhat\left(
\begin{tikzpicture}[baseline]
    \draw (3.5,.5) .. controls (4,0) .. (4.5,.5);
    \draw (3.5,-.5) .. controls (4,0) .. (4.5,-.5);
\end{tikzpicture}
\right)\right)