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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.

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