# Questions tagged [set-partition]

This tag is for questions relating to "partition of a set" or, "set-partition", which is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in exactly one subset.

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### Are there twice as many generalized partitions as partitions?

A partition of a set $S$ is a subset of the powerset of $S$, which covers $S$, is pairwise disjoint, and does not contain the empty set. If we drop the last condition, we get what I call a generalized ...
1 vote
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### Can you partition the set of 9 consecutive integers 1 to 9 in 2 sets, s.t. no member of either set is the mean of two other members of the same set? [duplicate]

Is it possible to partition the set $\Omega=\{1,2,3,4,5,6,7,8,9\}$ in two subsets $\Omega=A\cup B$, $A\cap B=\emptyset$, such that no member of either subset is the mean of two other members of the ...
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### Is the following Knapsack Variant NP-Hard?

The problem: Let $A_1 = \{a^1_1,\ldots,a^1_n\}, A_2 = \{a^2_1,\ldots,a^2_n\}, \ldots, A_k = \{a^k_1,\ldots,a^k_n\} \subset \mathbb{N}$ be $k$ sets of $n$ integers, and let $U,L \in \mathbb{N}$ be ...
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### Partition a positive integer sequence into subsequencies of equal weight

For a finite sequence of $N$ positive integers $a_1, a_2,.., a_N$ let us define its weight as $w (\{a_i\}) = \log(N) \cdot \sum_{1}^{N}{a_i}$. I want to partition such sequence into $K$ non-empty ...