-1

I am using a multiple variable summation formula, but I cannot seem to render it in mathematical text.

The principle is as follows: You have five hundred thousand units, they can be stored in any sized allotments, so in theory you could have five hundred thousand allotments (easy) to fifty allotments of variable potential sizes. The number of allotments is a Rand function, and the size of each allotment is a Rand function where they add up to the total units precisely.

Michael Harrington
  • 1
  • 1
  • allotments seems to mean there is a partition. But you must provide details on the Rand part of the question. What is the goal ? –  Sep 03 '16 at 14:08
  • Yes a partition, or allotment (shipping term, sorry) – Michael Harrington Sep 03 '16 at 20:34
  • ok, but why this random ? do you expect to pick some informations on the partition ? –  Sep 03 '16 at 20:37
  • It is to define all possible outcomes of the various allotments/partitions. – Michael Harrington Sep 03 '16 at 20:58
  • This has a real life representation I am trying to create, but I lack the skills to create the mathematical expression. My math is intuitive based, so it suffers at times when I have to create a formula. – Michael Harrington Sep 03 '16 at 22:24
  • Partitions may be computed directly. If you want to simulate some random process with random partitions, it is very hard to get a good small sample without knowing the precise context. The numbers become quickly very big. See this nice question on partitionning Repeatedly taking mean values of non-empty subsets –  Sep 03 '16 at 22:48
  • Very big numbers is what I hope to achieve. In fact if it can pass a googel I would laugh with joy. However I need the mathematical expression before I can start the computations. – Michael Harrington Sep 03 '16 at 23:10

1 Answers1

-1

https://brilliant.org/wiki/partition-of-an-integer/

This is close, but not quite.

In the example cited they show

  • 5
  • 4 | 1
  • 3 | 2
  • 3 | 1 | 1
  • 2 | 2 | 1
  • 2 | 1 | 1 | 1
  • 1 | 1 | 1 | 1 | 1

Where I am of the need to process it like this:

  • 5
  • 4 | 1
  • 1 | 4
  • 3 | 2
  • 2 | 3
  • 3 | 1 | 1
  • 1 | 3 | 1
  • 1 | 1 | 3
  • 2 | 2 | 1
  • 2 | 1 | 2
  • 1 | 2 | 2
  • 2 | 1 | 1 | 1
  • 1 | 2 | 1 | 1
  • 1 | 1 | 2 | 1
  • 1 | 1 | 1 | 2
  • 1 | 1 | 1 | 1 | 1

So where the Partitions of an Integer show a value of 7, my 'variation' would show 16.

It appears this is a new direction in Partitions of an Integer, therefore the answer is not in existing math.

Michael Harrington
  • 1
  • 1