Parenthesization/Examples
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Examples of Parenthesization
Parenthesization of Word of $2$ Elements
A word of $2$ elements can be parenthesized in only $1$ distinct way:
- $\quad \paren {a_1 a_2}$
Parenthesization of Word of $3$ Elements
A word of $3$ elements can be parenthesized in $2$ distinct ways:
- $\quad a_1 \left({a_2 a_3}\right)$
- $\quad \left({a_1 a_2}\right) a_3$
Parenthesization of Word of $4$ Elements
A word of $4$ elements can be parenthesized in $5$ distinct ways:
- $\quad a_1 \paren {a_2 \paren {a_3 a_4} }$
- $\quad a_1 \paren {\paren {a_2 a_3} a_4}$
- $\quad \paren {a_1 a_2} \paren {a_3 a_4}$
- $\quad \paren {a_1 \paren {a_2 a_3} } a_4$
- $\quad \paren {\paren {a_1 a_2} a_3} a_4$