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#151 2012-05-02 03:24:47

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Naturals.


“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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#152 2012-05-02 03:47:02

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions


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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#153 2012-05-02 03:49:58

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

How did you get that?


“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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#154 2012-05-02 03:52:51

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

It is in any combinatoric book. Partitions are huge since Euler's time.

http://en.wikipedia.org/wiki/Partition_ … _theory%29


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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#155 2012-05-02 05:57:06

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Ok,so the other book was right. I just couldn't understand rhe meaning behind it.


“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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#156 2012-05-02 07:36:10

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

Both are good.


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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#157 2012-05-02 08:20:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Which both? You don't know which the other book is.

Have you got any of those fruit problems?


“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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#158 2012-05-02 08:23:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

What fruit problems? What other book?


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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#159 2012-05-02 08:35:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Something whit choosing apples,pears,oranges,etc. so that some conditions are satisfied.


“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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#160 2012-05-02 08:40:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

That will be a very hard one to solve.


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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#161 2012-05-02 08:50:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Do you have any problems of that kind?


“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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#162 2012-05-02 08:51:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

Dozens but none of them are as tough as that one.


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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#163 2012-05-02 08:55:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

No. That is an outline of the type of problems. Can you post some of those?


“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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#164 2012-05-02 08:57:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

Oh, I thought that the some conditions were not to be given to you.


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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#165 2012-05-02 08:58:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

No,no. They are given. So could you post some of those problems?


“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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#166 2012-05-02 08:59:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

How about you post it since you are looking at 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.

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#167 2012-05-02 09:06:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Here it is,but it is the only one I have:

In how many ways can you fill a bag with n fruits,if you have only apples,pears,bananas and oranges and the following must be true:
1)The number of apples is even;
2)The number of pears is divisible by 5;
3)There are at most 4 oranges;
4)There is at most one banana.

I know how to do this one,so I would like some more complicated conditions.

Last edited by anonimnystefy (2012-05-02 09:07:45)


“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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#168 2012-05-02 09:08:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

You know how? I am from Missouri!


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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#169 2012-05-02 09:09:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Aren't you from Nevada?


“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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#170 2012-05-02 09:13:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

Me Pappy is from Alabama which is darn close to Missouri. Also I drove through that state once and had a darn good T-Bone steak.


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.

Offline

#171 2012-05-02 09:13:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Wait,are you questioning my ability to solve this?


“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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#172 2012-05-02 09:14:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

Missouri is called the "Show Me State," so...


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.

Offline

#173 2012-05-02 09:19:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Aham... The first GF has only even powers so it's 1/(1-x**2).

The second one has only powers that are divisible by 5 so it's 1/(1-x**5).

The third one has only powers from 0 through 4 i.e. 1+x+x**2+x**3+x**4.

The last,but not least,the GF that has only powers 0 and 1 i.e. 1+x.

We multiply them out,se that the coeff with x**n is n+1 so that is our answer.


“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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#174 2012-05-02 09:24:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,727

Re: Generating Functions

The last two are correct but put them in closed form.


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.

Offline

#175 2012-05-02 09:28:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,603

Re: Generating Functions

Oh,yeah. (1-x**5)/(1-x) and 1+x.


“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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