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What is wrong with my summation formula?

by DerekZ10
Tags: formula, summation
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DerekZ10
#1
Mar7-14, 01:29 AM
P: 4
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



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


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



Here is what I've formed, written out:


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


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:




The values are correct and what Chegg is showing. What have I done wrong in my equation?
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gopher_p
#2
Mar7-14, 02:00 AM
P: 462
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?
DerekZ10
#3
Mar7-14, 02:29 AM
P: 4
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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