Changes

Either one of the denotation maps induces the same partition of <math>S\!</math> into RECs, a partition whose structure is suggested by the following two sets of strings:

Either one of the denotation maps induces the same partition of <math>S\!</math> into RECs, a partition whose structure is suggested by the following two sets of strings:

: {<code>" ", "(( ))", "(( )( ))", ...</code>},

{| align="center" cellpadding="10" width="90%"

 

: {<code>"( )", "( )( )", "((( )))", ...</code>}.

<math>\begin{matrix}

& {}^{\backprime\backprime} \texttt{~}        {}^{\prime\prime},

& {}^{\backprime\backprime} \texttt{((~))}    {}^{\prime\prime},

& {}^{\backprime\backprime} \texttt{((~)(~))} {}^{\prime\prime},

& \}

& {}^{\backprime\backprime} \texttt{(~)}    {}^{\prime\prime},

& {}^{\backprime\backprime} \texttt{(~)(~)}  {}^{\prime\prime},

& {}^{\backprime\backprime} \texttt{(((~)))} {}^{\prime\prime},

\end{matrix}</math>

|}

These are of course the parenthesis strings that correspond to the rooted trees that are shown in the lower right corner of the Figure.

These are of course the parenthesis strings that correspond to the rooted trees that are shown in the lower right corner of the Figure.