What is alternative parenthesizations? I'm a person using english as the second language and reading CLRS book at a slow pace due to my poor english. I have a problem with understanding the meaning of the word 'alternative'. In page 303 on CLRS, says:


  we should convince ourselves that exhaustively checking all possible parenthesizations does not yield an efficient algorithm.Denote the number of alternative parenthesizations of a sequence of n
  matrices by P(n). Since we can split a sequence of n matrices between
  the kth and (k+1)st matrices for any k = 1,2,...,n-1 and then
  parenthesize the two resulting subsequences independently, we obtain
  the recurrence ...(omitted)


What is the word 'alternative parenthesizations'? is this word equivalent to the 'all possible parenthesizations' in the above block quote? searching dictionary for the word 'alternative' is not helpful to me. 
Thank you in advance.
Depending on the context, "all alternative parenthesizations" means either "all possible parenthesizations" or "all possible parenthesizations apart from the one we were just talking about."

The sense of the word "alternative" being used here is "one of two or more available possibilities."