All Questions
Tagged with integer-partitions integers
5
questions with no upvoted or accepted answers
3
votes
0
answers
44
views
By which scheme should I add the elements in series $(\sum n^{-2})^2$ and $\sum n^{-4}$ to show their rational equivalence?
We know that $\sum n^{-2}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\dots=\frac{\pi^2}{6}$ and $\sum n^{-4}=\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\dots=\frac{\pi^4}{90}$ from "high mathematics" ...
- 253
1
vote
0
answers
42
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Algorithm to find the distinct representations of the integer $n$ as a sum of $k$ non-negative p^(th) integer powers.
I am a user of Wolfram Mathematica and in that software there is a function called: PowersRepresentations. This function returns lists of integers $0\le n_1\le n_2\le\dots\le n_k$ such that $n_1^p+n_2^...
- 21
1
vote
0
answers
115
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Notation for "factorials" of integer partitions?
Let $\lambda = (\lambda_1, \lambda_2, \ldots, \lambda_k)$ be a partition of $n $, $\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_k > 0$.
Is there accepted notation (e.g. in the literature) for ...
- 2,579
1
vote
1
answer
271
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Count the number of ways n different-sided dice can add up to a given number
I am trying to find a way to count the number of ways n different-sided dice can add up to a given number.
For example, 2 dice, 4- and 6-sided, can add up to 8 in 3 different ways: ($(2,6),(3,5),(4,4)...
- 1,013
0
votes
0
answers
20
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Find minimum integer such that any integer \in [1, n] can be constructed from its consequent subsums
For example, here's (SPOILERS) breakdown for $1143$, which is the solution for $n = 9$
$\underline{1}143$
$\underline{11}43$
$114\underline{3}$
$11\underline{4}3$
$1\underline{14}3$
$\underline{114}3$...
- 230