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2-split of $n$ is $\left\{ \lfloor \frac{n}{2} \rfloor,\lceil \frac{n}{2} \rceil \right\}$. What about 3, 4, ...?

Clarification: $k$-split of $n$ is an ordered integer sequence $\left\{ a_1,\cdots,a_k \right\}\quad \text{s.t.}$ $0\le a_1\le\cdots\le a_k$ $a_1+\cdots+a_k=n$ ${\left(a_k-a_1\right)}$ is minimized. ...
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