Questions tagged [integer-partitions]
Partitions of an integer n are different ways of writing n as sum of smaller integers.
11
questions
3
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1answer
58 views
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. ...
4
votes
2answers
149 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 ...
1
vote
2answers
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 ...
0
votes
1answer
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. ...
1
vote
1answer
65 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 ...
-1
votes
3answers
1k views
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 ...
2
votes
0answers
88 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
votes
1answer
152 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
votes
1answer
126 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,...
1
vote
1answer
821 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
votes
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=...
