Definition:Parenthesization

Definition
Let $\circ$ be a product defined on a set $S$.

Let $a_1 \circ a_2 \circ \cdots a_i \circ \cdots \circ a_n$ denote a word in $S$ for some $n > 2$.

To distinguish all possible products of $a_1, a_2, \dotsc, a_n$, parentheses are inserted into the word.

A set of parentheses applied on a product is called a parenthesization of that word.