1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Combinatorics Question

  1. Nov 23, 2012 #1
    So the question was, Let x > 0.

    Prove that x[itex]^{n}[/itex] = [itex]\sum[/itex] [itex]\frac{x!}{x!-k!}[/itex] S(n, k).

    Where the sum goes from k = 1 to n and S(n, k) is th Stirling numbers.

    I believe I have proven what I needed to, but my question is why does x have to be greater than 0? Couldn't we define a function that maps [n] to {-x, ......, 1}.
    Last edited: Nov 23, 2012
  2. jcsd
  3. Nov 23, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Is this equation accurate? The kth term blows up when x = k! for some k in {1,2,...,n}.

  4. Nov 23, 2012 #3
    that should be an x! on the bottom... ill fix that
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Combinatorics Question Date
Non-Homework Combinatorics Question for a Legal Brief Apr 22, 2015
Combinatorics Questions Feb 2, 2015
Probability/Combinatorics Question Sep 17, 2014
Combinatorics question Apr 21, 2014
Combinatorics back-substitution Question Oct 18, 2013