1
$\begingroup$

How to find a function for calculating the number of well form brackets (for "n" pairs of brackets) using generating function? This is a probably a routine problem for some people, but I haven't got any resource on generating function.

  • 0
    What are well formed brackets? A series of parentheses that have the same number of opens as closes? Wouldn't that just be $\binom {2n}{n}$ for a string $2n$ long?2011-05-13
  • 6
    A must read on generating functions is Wilf's book www.math.upenn.edu/~wilf/gfology2.pdf2011-05-13
  • 3
    @Ross: Probably it means that you at any stage must have more left than right brackets, in which case the answer is given by the Catalan numbers.2011-05-13
  • 0
    @Hans: I think you are right.2011-05-13

1 Answers 1

3

If Hans Lundmark is right, you could see Wikipedia on the Catalan numbers, where the generating function is given under "Proof of the Formula" There are also many references in OEIS