All Questions
4
questions
1
vote
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Result on partitions with distinct odd parts
Let $pdo(n)$ be the number of partitions of n into distinct odd parts. Then $p(n)$ is odd if and only if $pdo(n)$ is odd.
I am well aware that a proof of this is available here but I want to do it ...
- 13
0
votes
0
answers
174
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Compatible partitions with laws of compositions?
An exercise from Artin's Algebra:
Let S be a set with a law of composition: A partition $\Pi_1 \cup \Pi_2 \cup ...$ of S is compatible with the law of composition if for all i and j, the product ...
user198044
0
votes
1
answer
53
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Question about the partitions of a natural number
There is a function that counts the number of partitions of with $n$ digits?
I am aware of the partition function studied by Ramanujan, but what I want is a subset of the partitions that are counted ...
- 2,505
2
votes
0
answers
338
views
Dominance ordering on partitions of $n$.
Denote the collection of partitions of $n$ by $\mathcal{P}(n)$, with the property that for $\lambda = (\lambda_1,\cdots,\lambda_s)\in\mathcal{P}(n)$ we have
$$\lambda_1\geq \cdots \geq \lambda_s \geq ...
- 754