Given a vector $v$ with non-negative integer coordinates, is there a technical term for an unordered tuple of vectors $(v_1,\dots, v_k)$ with non-negative integer coordinates such that
$v_1+\dots+v_k = v$?
I would have liked to have called it a Vector Partition of $v$, but that term seems to be used for a decomposition a vector as a linear combination with non-negative integral coefficients of a fixed set of vectors.
An authoritative reference for the usage would also be welcome.
The closest term in the literature, I think, is multiway number partitioning. A recent work is out here. Note that the work even discusses about amore general problem- of partition the list so that the sum is as close as possible.