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## #1 2013-04-12 16:55:52

eldoci
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### Calculating combinations

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 (2013-04-12 21:28:38)

## #2 2013-04-12 17:39:39

bobbym

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### Re: Calculating combinations

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.
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.

## #3 2013-04-12 21:27:34

eldoci
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### Re: Calculating combinations

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 23:17:29)

## #4 2013-04-12 22:07:58

bobbym

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### Re: Calculating combinations

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.
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.

## #5 2013-04-12 22:12:31

eldoci
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### Re: Calculating combinations

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

## #6 2013-04-12 22:17:33

eldoci
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### Re: Calculating combinations

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

## #7 2013-04-12 22:19:30

bobbym

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### Re: Calculating combinations

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.
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.

## #8 2013-04-12 22:34:51

eldoci
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### Re: Calculating combinations

yes | | is the absolute value

## #9 2013-04-12 22:43:02

bobbym

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### Re: Calculating combinations

Hi;

Just a bit more, Where do the combinations come 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.

## #10 2013-04-12 23:15:41

eldoci
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### Re: Calculating combinations

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

## #11 2013-04-12 23:39:57

bobbym

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### Re: Calculating combinations

Hi;

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

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.

eldoci
Novice

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Thank you

## #13 2013-04-13 03:34:18

bobbym

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### Re: Calculating combinations

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.

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.