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#76 2012-04-30 14:55:33
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#77 2012-04-30 14:58:00
- anonimnystefy
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Re: Generating Functions
Seems so. Sorry for asking this,but,how do we prove that the answer we get is what we wanted?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#78 2012-04-30 15:03:34
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#79 2012-04-30 22:36:56
- anonimnystefy
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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?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#80 2012-04-30 22:38:30
- bobbym
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Re: Generating Functions
That does not make sense.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#81 2012-04-30 22:39:47
- anonimnystefy
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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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#82 2012-04-30 22:40:52
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#83 2012-04-30 22:41:48
- anonimnystefy
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Re: Generating Functions
Either way-Is there a hand proof that using GFs like that does the job right?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#84 2012-04-30 22:44:27
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#85 2012-04-30 22:45:34
- anonimnystefy
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Re: Generating Functions
I don't understand you.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#86 2012-04-30 22:55:00
- bobbym
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Re: Generating Functions
Talking about gfs is different then post #77
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#87 2012-04-30 22:57:11
- anonimnystefy
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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?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#88 2012-04-30 22:58:48
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#89 2012-04-30 23:07:55
- anonimnystefy
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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:
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. 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#90 2012-04-30 23:13:02
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#91 2012-04-30 23:17:11
- anonimnystefy
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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 23:17:39)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#92 2012-04-30 23:26:36
- bobbym
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Re: Generating Functions
Expanded out?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#93 2012-04-30 23:27:41
- anonimnystefy
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Re: Generating Functions
Doesn't matter.I can expand it later if I it doesn't expand itself on output.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#94 2012-04-30 23:29:33
- bobbym
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Re: Generating Functions
Question first:
How would you display this:
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#95 2012-04-30 23:31:27
- anonimnystefy
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Re: Generating Functions
I don't know what you mean.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#96 2012-04-30 23:34:43
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#97 2012-04-30 23:37:58
- anonimnystefy
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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.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#98 2012-04-30 23:39:10
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#99 2012-04-30 23:42:19
- anonimnystefy
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Re: Generating Functions
The code in #89 would be for that.
And my input would be:
CombiGF([6])
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#100 2012-04-30 23:44:18
- bobbym
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.