# Questions tagged [integer-partitions]

Use this tag for questions related to ways of writing a positive integer as a sum of positive integers.

854 questions
12 views

20 views

35 views

### Is my answer correct? Partitioning numbers

How many ways are there to write the number 7 with the summands: 1, 2, and 3? For example, there are 7 ways to write the number 4: {1 + 1 + 1 + 1} x 1 {2 + 1 + 1} x 3 {3 + 1} x 2 {2 + 2} x 1 I ...
301 views

74 views

### Decomposing an integer number into up to N (not necessarily prime) numbers with minimal sum

I am writing a program that processes data based on an integer factor. The process can either be done at once, or in multiple stages. For example, one stage with factor 500 could be replaced by three ...
13 views

### On some constrained partitions of $k$-multiperfect numbers

Let $n$ be a $k$ -multiperfect number. Do we know an upper bound for the number of partitions of $n$ whose all summands are at the same time multiples of $k$ and the sum of distinct ...
186 views

### partitions of positive integer $n$ with respect to a multiset

Recently, I think on a new problem related to partitions. Let $n$ be a non-negative integer and $\mathbb{A}=\{a_1,\ldots,a_k\}$ be a multiset with $k$ not necessarily distinct positive integers. We ...
### Combinatorial Proof that $p(n)/(1+\epsilon)^n \to 0$
I was thinking this morning about the identity $\prod_{n=1}^{\infty} \left( \frac{1}{1-q^n} \right) = \sum_{n=0}^{\infty} p(n) q^n$. The product on the left converges for $|q|<1$, which implies ...