What is wrong with my summation formula?

  • Thread starter DerekZ10
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  • #1
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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
46rbw7h.png



From: Discrete Mathemeatics and Its Applications 7th Edition Rosen pg. 512
UY3OIud.png


Random Chegg Problem from Google Search I'm using to verify with:
wJUOwNS.png



Here is what I've formed, written out:
NqrU3l3.jpg


In the TI nSpire CX CAS, it's written like this:
iwIkElK.jpg


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:

gyDYmtH.jpg



The values are correct and what Chegg is showing. What have I done wrong in my equation?
 

Answers and Replies

  • #2
575
76
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?
 
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  • #3
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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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