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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

If we have a matrix with N elements, where each element can take values G ( 0-255), we can obtain 256 power N possibilities of matrixes.

The derivative of each matrix is calculated as follows:

S=∑_(n=1)^(N-1)▒df(n)/dx=∑_(n=1)^(N-1)▒〖| f(n+1)-f(n)|〗

Since 0≤ df(n)/dx≤255 the minimum and maximum values of s are:

max S = (N-1)×255

min S = 0

I need to find how many matrixes have the same S.

Can anybody help me?

Thank you.

*Last edited by eldoci (2013-04-11 23:28:38)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

Welcome to the forum. I am sorry, I can not make out your equation for S. Can you latex it or take a snapshot?

What is f?

**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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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

Thank you for replying.

I am Sorry for not using latex.

Maybe you can understand the formula of S in this form:

S = sum (df(n)/d(x))=sum(|f (n+1)- f(n)|) for n=1,2,3...(N-1)

f(n) is the value of X in the position n of the matrix.

During calculations I have noticed that for S=0 we always get G combinations ( G matrices).

S=max we always get 2 combinations (matrices)

S=1 we get 2(N-1)*(G-1) (matrices)

Now i need to find a formula that gives me the combinations for any S.

I hope this makes the problem more clear for you.

*Last edited by eldoci (2013-04-12 01:17:29)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

I hope this makes the problem more clear for you.

I still need more clarification.

f(n) is the value of X in the position n of the matrix.

How does n do that? A matrix needs 2 numbers, a row and a column to specify a position. How do you do that with one?

**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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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

You are right about the matrix, it has 2 variables, x and z, but for simplicitz we supose that we have 1 dimension matrix( a vector) with 1 row and N elements on it

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

You are right about the matrix, it has 2 variables, x and y, but for simplicity we suppose that we have 1 dimension matrix( a vector) with 1 row and N elements on it.

For example:

for the matrix [1 0 0 2]

S= |0-1|+ |0-0|+ |2-0|=3

f(n0)=1 f(n1)=0 f(n2)=0 and f(n3)=2

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

sum(|f (n+1)- f(n)|)

| |

That is an absolute value?

**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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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

yes | | is the absolute value

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

Just a bit more, Where do the combinations come in?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

If we have a matrix with N elements, where each element can take values G ( 0-255), we can obtain 256 power N possibilities of matrixes ( combinations of elements).

I need to calculate: how many element combinations of the matrix ( no of matrixes) can be obtained with the same S

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

Okay, I think I have enough. I will post if I get something.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

Thank you

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi;

I have been unable to so far find any expression for that matrix. Are you sure there is one and can you say where the problem comes from.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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