(along different lines than ours), but it does not seem to have been widely cited.

$$\scalebox{0.67}{ \begin{tikzpicture}[grow=down]
                    \tikzstyle{level 1}=[sibling distance=120mm]
     \tikzstyle{level 2}=[sibling distance=40mm]
     \tikzstyle{level 3}=[sibling distance=10mm]
     \node {$\substack{1 \\ \ \\ \frac{6{\theta}}{{\theta}^4 + 6{\theta}^3 + 11{\theta}^2 + 6{\theta}}}$ }
     child{ node {$\substack{12 \\ \ \\ \frac{6{\theta}^2}{{\theta}^4 + 5{\theta}^3 + 6{\theta}^2}}$ } 
     child{ node {$\substack{123 \\ \ \\ \frac{3{\theta}^3}{{\theta}^4 + 3{\theta}^3}}$ }
     child{ node{$\substack{1234 \\ \ \\ \frac{{\theta}^4}{{\theta}^4}}$}}
       child{ node{1243}}
       child{ node{1342}}
       child{ node{2341}}
   }
   child{ node[gray]  {132 }
   child{ node{$\substack{1324 \\ \ \\ \frac{{\theta}^3}{{\theta}^3}}$} }
       child{ node{1423}}
       child{ node{1432}}
       child{ node{2431}}
   }
   child{ node[gray]  {231 }
   child{ node{$\substack{2314 \\ \ \\ \frac{{\theta}^3}{{\theta}^3}}$} }
       child{ node{2413}}
       child{ node{3412}}
       child{ node{3421}}
   }
 }
 child{ node[gray]  {21 } 
 child{ node {$\substack{213 \\ \ \\ \frac{3{\theta}^2}{{\theta}^3 + 3{\theta}^2}}$ }
 child{ node{$\substack{2134 \\ \ \\ \frac{{\theta}^3}{{\theta}^3}}$}}
       child{ node{2143}}
       child{ node{3142}}
       child{ node{3241}}
   }
   child{ node[gray]  {312 }
   child{ node{$\substack{3124 \\ \ \\ \frac{{\theta}^2}{{\theta}^2}}$} }
       child{ node{4123}}
       child{ node{4132}}
       child{ node{4231}}
   }
   child{ node[gray]  {321 }
   child{ node{$\substack{3214 \\ \ \\ \frac{{\theta}^2}{{\theta}^2}}$} }
       child{ node{4213}}
       child{ node{4312}}
       child{ node{4321}}
   }
 };
\end{tikzpicture}
}$$

In Figure \[f:treeex\] we have illustrated the prefix tree with ineligible prefixes shown in gray and strike probabilities given below each eligible prefix.

