# Questions tagged [integer-partitions]

Partitions of an integer n are different ways of writing n as sum of smaller integers.

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### Number of ways n can be written as sum of at least two positive integers

I found a solution in Python for this problem, but do not understand it. The problem is how many ways an integer n can be written as the sum of at least two positive integers. For example, take n = 5. ...
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### A problem on constrained combinatorics

Not sure if this is a proper place, but I really don't know where else to ask. I'm craving for an algorithm generating certain sequences of numbers (the problem comes from physics). I'm looking for ...
61 views

### A physical algorithm that finds all integer partitions of a number

If this is not the right forum for this question let me know. I am looking for a physical algorithm that can be easily followed by anyone not knowing much ...
65 views

### sub-optimal but fast partition generation

I have a set of N integers that I want to partition into m subsets. I want these subsets to be well-balanced wrt some criterion say that minimize the max difference between the size of all subsets. ...
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### Given a valid combination, how to get its index in the sequence of integer partition

This question is extended from this Algorithm to generate integer sets fulfills restrictions, in the answer I learned the formal term of this problem, and the recursive algorithm described in that ...
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### Divide N sticks among M boys as homogeneously as possible (ignoring order)

There are $N$ sticks. $N$ is an integer greater than zero. I want to divide it among $M$ boys. $M$ is also a positive integer. Partitioning $N$ among $M$ is easy, but doing it as evenly as possible is ...
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### Generating a distinct k-partition of n

Let us consider a specific case of an extended Kakuro puzzle. Given an integer $n$, we must form $n$ as the sum of $k$ distinct positive integers each less than or equal to $r$. From a mathematical ...
The refinement order on partitions of an integer $n$ can be defined as follows: $\lambda=(\lambda_1,\dots,\lambda_k)\leq\mu=(\mu_1,\dots,\mu_\ell)$ if there is a partition of the parts of $\lambda$ ...