Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is this sum exponential?

  1. Jul 16, 2009 #1
    Hello,

    I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?"

    Anyway, during solving this problem I came to this point:

    Is the following sum exponential in [itex]2n[/itex]?

    [tex]
    \sum_{x=0}^{n} \left( \begin{array}{cc} 2n \\ 2x \end{array} \right)
    [/tex]

    Are there some nice combinatorial identities which I overlooked that can be useful in this case?

    Thank you very much.
     
  2. jcsd
  3. Jul 16, 2009 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    If you leave out the 2's in the combinatorial symbol, the answer (as you probably know) is 2n. I would guess your sum is something like 2(2n-1), since you are missing about half the terms.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook