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What is wrong with my summation formula?

  1. Mar 7, 2014 #1
    Im trying to find a general formula I can store in my calculator that can find the number of onto (surjective) functions exists for a relation of when M is mapped to N.

    I can't seem to find a nice formula for it, but based on the below material I will show you what I have developed.

    From: Discrete Mathemeatics and Its Applications 7th Edition Rosen pg. 561
    [​IMG]


    From: Discrete Mathemeatics and Its Applications 7th Edition Rosen pg. 512
    [​IMG]

    Random Chegg Problem from Google Search I'm using to verify with:
    [​IMG]


    Here is what I've formed, written out:
    [​IMG]

    In the TI nSpire CX CAS, it's written like this:
    [​IMG]

    And as you can see, the chegg problem I'm trying to verify it with doesn't match!
    But I think it should! If I manually iterate the function like so:

    [​IMG]


    The values are correct and what Chegg is showing. What have I done wrong in my equation?
     
  2. jcsd
  3. Mar 7, 2014 #2
    Did you check that your summation formula matches the version that doesn't use sigma notation? i.e are all your ##m##s and ##n##s where they're supposed to be?
     
  4. Mar 7, 2014 #3
    Wow, good call! I don't know how I constantly was missing that the (m-k) portion that should have been (n-k). And I even had it right in the non iterative equation.
     
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