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#176 2012-05-03 07:31:45

bobbym
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Re: Generating Functions

Correct! So what is the problem?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#177 2012-05-03 07:35:30

anonimnystefy
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Re: Generating Functions

Nothing. You asked me to post it. I asked you then if you can post a more complicated one.


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

#178 2012-05-03 07:36:30

bobbym
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Re: Generating Functions

Nope! You know how to do it. They do not get more complicated than that in books.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#179 2012-05-03 07:39:27

anonimnystefy
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Re: Generating Functions

Can't you think of one?


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

#180 2012-05-03 07:41:16

bobbym
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Re: Generating Functions

That is the prototypical problem for that type that appears in books. It tests your ability to form the generating function. You can do it. There are two things left...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#181 2012-05-03 07:44:40

anonimnystefy
Real Member

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Re: Generating Functions

Which two things?


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

#182 2012-05-03 07:45:28

bobbym
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Re: Generating Functions

1) Getting the coefficient.

2) Knowing when and where to use the GF.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#183 2012-05-03 07:49:31

anonimnystefy
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Re: Generating Functions

Okay. The coeff can be found in two ways:
1)Computers. Nothing more to say about that.
2)Partial fractons and expand the GFs you get. Read off the general term from the GF you get when you sum all of those GFs you have after partial fractions.

There is no exact rule for the second one. It is I think mostly intuition,though some problems just look made for GFs and some look exactly opposite of that.


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

#184 2012-05-03 07:51:09

bobbym
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Re: Generating Functions

2) There are many other ways. gAr and I have discussed them.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#185 2012-05-03 07:52:38

anonimnystefy
Real Member

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Re: Generating Functions

I know. I am saying that it is mostly intuition (gained by experience of course) that determines wheter ir not GFs should be used.


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

#186 2012-05-03 07:55:20

bobbym
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Re: Generating Functions

No one can say. A brilliant guy I know asked whether every combinatoric question could be put into the form of a generating function. He posted that question to the best of the best of the best. He got no reply.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#187 2012-05-03 07:58:18

anonimnystefy
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Re: Generating Functions

If the answer is yes,then we should be able to find a GF for juan's matrix problem.


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

#188 2012-05-03 08:00:43

bobbym
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Re: Generating Functions

Me Pappy wrote:

If is a big word.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#189 2012-05-03 08:03:58

anonimnystefy
Real Member

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Re: Generating Functions

How lucky would I have been to ever have met Pappym.

Mathematics is based on lots of assumptions. We use Euclid's geometry,even though we live on a sphere.


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

#190 2012-05-03 08:06:10

bobbym
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Re: Generating Functions

He was the greatest m that ever lived.

As a person he was a lot like you.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#191 2012-05-03 08:08:54

anonimnystefy
Real Member

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Re: Generating Functions

Greater than Grandpappym?

How is he a lot like me as a person?


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

#192 2012-05-03 08:13:19

bobbym
Administrator

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Re: Generating Functions

GrandPappym was little more than a beast posing as a man.  Tremendously strong and powerfully built. He used his strength to dominate people.

How is he a lot like me as a person?

He was also rebellious in his youth. Unfocused and impatient, sort of like Luke Skywalker.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#193 2012-05-03 08:16:19

anonimnystefy
Real Member

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Re: Generating Functions

Wow,that really does sound like me!

Btw,I think I have over 6000 posts now.


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

#194 2012-05-03 08:17:16

bobbym
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Re: Generating Functions

Yes, you do. Congratulations.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#195 2012-05-03 08:19:21

anonimnystefy
Real Member

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Re: Generating Functions

Thank you,but it is not the number that counts.

Would you like to propose the next topic if you have nothing more to say about this one?


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

#196 2012-05-03 08:23:13

bobbym
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Re: Generating Functions

We had that discussion a long time ago.

Keep the thread open, New stuff will go in.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#197 2012-05-03 08:25:50

anonimnystefy
Real Member

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Re: Generating Functions

Yes. We had it twice. I do not remember the conclusions though.

Of course I will keep it open. I wouldn't close this one if (enter a reason here). I was just asking if you would like to post the next topic or should I.


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

#198 2012-05-03 08:27:18

bobbym
Administrator

Offline

Re: Generating Functions

No the discussion I am talking about was before you were a member. I was the lightweight in the group and no one paid any attention to what I said.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#199 2012-05-03 08:29:27

anonimnystefy
Real Member

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Re: Generating Functions

Do you know where that discussion is.

And you still haven't told if you want to open the new topic or should I.


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

#200 2012-05-03 08:34:39

bobbym
Administrator

Offline

Re: Generating Functions


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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