Tagged Questions
3
votes
1answer
34 views
cosets aren't forming a partition?
If you have a group $G$ and $H \leq G$, the cosets of $H$ should partition $G$.
Suppose $G=\mathbb{Z}_2\times\mathbb{Z}_4$ and $H=\langle (0,1)\rangle = \{(0,0), (0,1),(0,2),(0,3)\}$. Then both ...
0
votes
5answers
344 views
General questions about equivalence classes and partitions
1) If a set is partitioned into non-overlapping, non-empty subsets, then those subsets are equivalence classes. If each element in a set is unique, how can a set be partitioned into subsets with ...
3
votes
2answers
246 views
Partitioning a natural number $n$ in order to get the maximum product sequence of its addends
Sorry if i ask this question. probably it's already answered somewhere else but i didn't find it.
Suppose to have a natural number $n \ge 0$.
Given natural numbers $\alpha_1,\ldots,\alpha_k$ such ...
3
votes
2answers
157 views
The fibres of a map form a partition of the domain.
This is a question from the free Harvard online abstract algebra lectures. I'm posting my solutions here to get some feedback on them. For a fuller explanation, see this post.
This problem is from ...
3
votes
2answers
97 views
Generating sequences of numeric partitions
Definition: A tuple $\lambda = (\lambda_1, \ldots, \lambda_k)$ of natural numbers is called a numeric partition of $n$ if $1 \leq \lambda_1 \leq \cdots \leq \lambda_k$ and $\lambda_1 + \cdots + ...
