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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Be sure to tell if you get an idea!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

I have something. It will take some time.

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**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Can you post just the beginning steps?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

Calculation is running, it will take a while.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Post when it's done.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

Hi;

Procedure failed, I do not know why.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

What procedure?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

An attempt to develope an asymptotic form that would have eliminated the coefficient part of your maxima code.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Can you elaborate?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Instead of picking out the i - k power of x out of the expansion. For large k, I figured that expansion would approach (e^x)^5. The coefficient of x^(i-k) of that is 5^(i-k) / (i-k)!. For large k this would have replaced expanding a big polynomial raised to the 5th power. Unfortunately, it did not work.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Why not?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

I do not know. I tested it for k = 20, 30 , 40 , 50, 60, 100, 200. It did not asymptotically approach the exact answer.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

I guess that there are too many terms that contribute to the x^(i-k) term.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

I am not sure, I will think about it.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Hi bobbym

I got a reply. He said he does not need the solution if it just involves the standard bunch of methods.

Personally, I really do not think that that problem is the best one for showing how Markov chains can be used, but, it is his work, and I will not insist on it anymore.

I would still like to continue working on an analityc form here.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

Personally, I really do not think that that problem is the best one for showing how Markov chains can be used, but, it is his work, and I will not insist on it anymore.

I am not following you. He does not always use Markov chains. Your method is a standard method, even though I do not know what he means by that.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Hi bobbym

What I meant to say is, if he wanted to show how Markov chains work, he should've done it on a smaller and bit simpler problem.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

Hi;

I am not suggesting that you persist in publishing. That is a decision that is up to you, but the purpose of that pdf is not to just demonstrate Markov chains. It is to solve dice problems.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

Again you misunderstood me. He said that, if the answer is a classical one, then he doesn't need it. He obviously wants the second part of 10th problem to be with Markov chains.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

That is impossible, the next one would require a 4097 x 4097 matrix!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I meant for the 3 case.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I think we can't approximate it using e^(5x), since we are using coefficients beyond the upper limit of the egf. Below is the probability plot for n=45.

Hi anonimnystefy,

Standard bunch of methods? Did he mean he has solution for that already, but did not publish in his pdf?

*Last edited by gAr (2013-02-17 21:35:14)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

He already solved the 3 case. It took a 730 x 730 matrix. He will never get a general answer as you did using Markov chains.

*Last edited by bobbym (2013-02-17 21:35:33)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

bobbym wrote:

He already solved the 3 case. It took a 730 x 730 matrix. He will never get a general answer as you did using Markov chains.

Yes, but it seems he wanted to show how Markov chains work on particularly that problem.

Anyway, there is no point in discussing it any more. Have you found anything else that could help us with the GF?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,588

Hi;

I am not unhappy with your decision, as I said it is your choice. You should be advised though that someone from another forum will eventually see your solution, change it a bit and call it his own.

I could possibly shorten the computation a bit but I do not want to do that. I would prefer to eliminate the gf or to just leave it as it is.

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