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#226 2012-05-03 06:34:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

That is why it should not be. They count permutations.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#227 2012-05-03 06:48:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Wait until later this evening or tomorrow,and we will discuss this properly.


“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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#228 2012-05-03 06:50:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Now you are talking turkey. Armed with your CAS you will be 100 times stronger.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#229 2012-05-03 06:53:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Of course! I think I am starting to like Maxima.


“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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#230 2012-05-03 07:58:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Hi bobbym

I got 887/55986


“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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#231 2012-05-03 08:03:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

I am not getting that.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#232 2012-05-03 08:05:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

What do you get?


“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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#233 2012-05-03 08:06:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

First put an x = 1 into your expanded answer what do you get?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#234 2012-05-03 08:08:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

55986


“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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#235 2012-05-03 08:13:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Hmmm. Since that is a probability gf and each x powers coefficient is a probability.  When you put x = 1 you are summing the gf. Since that is all the possibilities what should that sum be?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#236 2012-05-03 08:15:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Hi bobbym

I didn't make a probability counting GF,but a possibility counting one.


“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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#237 2012-05-03 08:16:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Not a good idea because you will not be able to turn that into a probability.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#238 2012-05-03 08:17:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

But when I put x=1 I get all the possibilities amd the coeff of x**17 gives me the favorable cases.


“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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#239 2012-05-03 08:22:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Maybe it does but what is a probability?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#240 2012-05-03 08:23:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

P=favorable/all possible.


“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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#241 2012-05-03 08:28:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

It is a ratio. It is a fraction. Now I ask you what do you put on the bottom of your number to get that ratio?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#242 2012-05-03 08:29:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

All possible outcomes?


“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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#243 2012-05-03 08:30:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

55986 / All possible outcomes


I put that into M and he just spit it out.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#244 2012-05-03 08:31:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

That is the number I got too for the possible outcomes.


“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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#245 2012-05-03 08:34:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

How did you compute this?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#246 2012-05-03 08:36:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

No,I got the number 55986 to be down.


“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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#247 2012-05-03 08:39:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Then what is on top?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#248 2012-05-03 08:42:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

887.


“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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#249 2012-05-03 08:45:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

That is not correct.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#250 2012-05-03 08:48:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Sorry,it's 3743.

Last edited by anonimnystefy (2012-05-03 08:49:10)


“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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