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#76 2012-04-29 16:55:33

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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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#77 2012-04-29 16:58:00

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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


“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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#78 2012-04-29 17:03:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

Online

#79 2012-04-30 00:36:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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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#80 2012-04-30 00:38:30

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

Online

#81 2012-04-30 00:39:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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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#82 2012-04-30 00:40:52

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

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.

Online

#83 2012-04-30 00:41:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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


“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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#84 2012-04-30 00:44:27

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

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.

Online

#85 2012-04-30 00:45:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

I don't understand you.


“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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#86 2012-04-30 00:55:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

Talking about gfs is different then post #77


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.

Online

#87 2012-04-30 00:57:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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


“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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#88 2012-04-30 00:58:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

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.

Online

#89 2012-04-30 01:07:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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. hmm


“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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#90 2012-04-30 01:13:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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


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.

Online

#91 2012-04-30 01:17:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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)


“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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#92 2012-04-30 01:26:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

Expanded out?


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.

Online

#93 2012-04-30 01:27:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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


“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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#94 2012-04-30 01:29:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

Question first:

How would you display this:


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.

Online

#95 2012-04-30 01:31:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

I don't know what you mean.


“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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#96 2012-04-30 01:34:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

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.

Online

#97 2012-04-30 01:37:58

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

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


“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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#98 2012-04-30 01:39:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

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.

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.

Online

#99 2012-04-30 01:42:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Generating Functions

The code in #89 would be for that.

And my input would be:

CombiGF([6])


“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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#100 2012-04-30 01:44:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,645

Re: Generating Functions

Why are you using a procedural form in a CAS?


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.

Online

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