combinatorics/complex numbers/partitions

nullified

New member
Joined
May 21, 2013
Messages
4
I have a problem along those lines..

Say I have the following complex numbers:

4 + 1i
3 + 1i
3 + 3i
2 + 2i

I was adding them all together to get one result: 12 + 7i. But I need to go back to the original four complex numbers.. So my question has two parts:

1. If I can go back from 12 + 7i to the original four, what is the best way to do that?
2. If I can't do #1, how do I add these together in order to both arrive at only one complex number and go back to the original four?

Thanks,
 
I have a problem along those lines..

Say I have the following complex numbers:

4 + 1i
3 + 1i
3 + 3i
2 + 2i

I was adding them all together to get one result: 12 + 7i. But I need to go back to the original four complex numbers.. So my question has two parts:

1. If I can go back from 12 + 7i to the original four, what is the best way to do that?
2. If I can't do #1, how do I add these together in order to both arrive at only one complex number and go back to the original four?

Thanks,

What do you mean by "go back"??
 
What do you mean by "go back"??

Sorry, my words are not as exact as my numbers and equasions; that tends to make things mis-understood... If you don't feel like reading through the explanation, I found that trying to solve this particular problem is unreasonable at this time...

What I was meaning was this:

I use partitions to solve particular 'packing problems' with numerics instead of geometry. I will illustrate what I mean by the following example of compressing the numbers and then imploding them - 'going back' to the original complex numbers:

(original four)
4+1i
3+1i
3+3i
2+2i

(adding them together - this 'packs' them into one complex number)
(4 + 1i) + (3 + 1i) + (3 + 3i) + (2 + 2i) = 12 + 7i

Here's the problem - 'going back' or 'unpacking' or 'imploding' them back to the original four:

12 + 7i = 4+1i, 3+1i, 3+3i, 2+2i.

However, my question is already answered: I was trying to find a way to do this without brute-forcing (trying all possible sequences). I already had unique complex numbers, so that part was possible without error but I introduced compositions requirements for these sets by having two connected sets that then rely on correct ordering. This means that the numbers not only need to 'go back' to the original four complex numbers, but it all needs to be in the correct sequence. Not only that - it needs to be in the correct sequence across two different numerical points...

That made it unreasonable to solve, because there are numerous more compositions than partitions; and that makes solving this particular problem unreasonable. The computations required are not a good fit for this particular problem...

I'll explain the problem below in numerics, so you don't have to understand my slurred/misleading... statements of words...

The problem is: given a set of complex numbers, use partitioning methods to represent them in a single complex number, then be able to arrive from the single complex number back to the original set...

(4+1i)+(3+1i)+(3+3i)+(2+2i) = 12+7i = 4+1i, 3+1i, 3+3i, 2+2i - assuming I were to somehow find a non-trivial way to do this by combining partitioning and compositions...
(4+1i)+(3+1i)+(3+3i)+(2+2i) = 12+7i = 4+3i, 3+2i, 3+1i, 2+1i - this is the result of reversing the 12+7i part using methods of partitioning. As you can see, it yields all incorrect results except for 3+1i. Partitioning doesn't care about order. So it doesn't know order. Therefore, there's no way to tie it back except to sort the numbers, which would yield incorrect results regardless of sorting (even sorting the other way, 2+3i, 3+2i, 3+1i, 4+1i, still gives two incorrect results)

Sorry if I wasted some of your time - I should have realized this before I posted... I think I'm going to go back and re-study a lot of the old math that I used to know. I think I've forgotten most of it.
 
Top