Questions tagged [integer-partitions]

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

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2answers
144 views

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 ...
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2answers
59 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 ...
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1answer
60 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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0answers
48 views

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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2answers
953 views

Divide N sticks among M boys as evenly as possible

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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0answers
86 views

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 ...
5
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1answer
147 views

Practical Implementation for Refinement Order on Integer Partitions

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 $\lambda$ ...
2
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1answer
125 views

Finding a specific “balls-into-bins” partition given its index in the lexicographical ordering

Given numbers $n,k\in \mathbb{N}$, we consider $\mathcal P$ to be the set of all possible partitions of $n$ balls into $k$ bins. Alternatively, $\mathcal P$ is the set of all $k$-ary vectors in $\{0,...
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1answer
799 views

Applications in Computer Sciences of Partition Functions

A partition function computes the number of ways an integer $n$ can be represented as the sum of $m$ other integers. For some value $n$, we have a partition function $p(n)$. These were studied ...
5
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4answers
2k views

Divide an integer into the sum of consecutive positive numbers

Today I am trying to solve an classical problem: For any $n\in \Bbb{N}^+$, If it can be represent as the sum of consecutive positive numbers, find out them. For example: $$15 = 1+2+3+4+5$$ $$15=...