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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Yes, that is all there is to solving those types of permutation problems. Easy with generating functions hard with the school method.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

Seems so. Sorry for asking this,but,how do we prove that the answer we get is what we wanted?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Remember the guy who did not want to do anymore math so he learned computers. That is how.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

You mean you?

Computers again? I don't think that using this in class will be any good if I can prove it gets the right answers without a hand method.Ironic,huh?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

That does not make sense.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

If I am going to use this method in class,I need to be able to show it works by hand methods.It really doesn't make sense,but it s how it is.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Nope, the computer backs up the hand method.

People who only use hand methods rarely get a combinatorics problem correct.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

Either way-Is there a hand proof that using GFs like that does the job right?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Different question, they are both hand methods. That is why I do not remember them.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

I don't understand you.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Talking about gfs is different then post #77

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

No,I meant-How do I prove that the answer we got with GFs is the the correct one by hand methods?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Prove? That is a funny word. Generally when you do a piece of algebra you do not have to prove it. The work is the proof.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

Well,I am not sure if my prof is gonna be happy if I don't show somehow that the number that I got using GFs is correct.

Can you look something up to tell me what is wrong with this Maxima code:

```
CombGF(list):=block([i,j,a,m,s],
i=1,
m=1,
while i<=length(list) do
[
a=get(list,i),
j=1,
s=0,
while j<=a do
s=s+x^j,
m=m*s,
i=i+1
],
return(m)
);
```

It compiles,but doesn't run properly.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

You wrote it? What is the output supposed to look like?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

Yes,I wrote it.

It should give me a generating function in x.E.g.:

CombiGF([1,1,1,2]);

should give:

PS I changed the code line:

s=s+x^j,

to

s=s+x^j/j!,

*Last edited by anonimnystefy (2012-04-30 01:17:39)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Expanded out?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

Doesn't matter.I can expand it later if I it doesn't expand itself on output.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Question first:

How would you display this:

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

I don't know what you mean.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Same thing. I wish to have the gf of a single dice. How do you do it?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

It doesn't do the ordinary GF.It does the exp GF for the type of problem you've given me before.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

What I am saying is would you write a loop like you have done to do that?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,655

The code in #89 would be for that.

And my input would be:

CombiGF([6])

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,432

Why are you using a procedural form in a CAS?

**In mathematics, you don't understand things. You just get used to them.**

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