Definition:Composition (Combinatorics)

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Definition

A $k$-composition of a (strictly) positive integer $n \in \Z_{> 0}$ is an ordered $k$-tuple:

$c = \left({c_1, c_2, \ldots, c_k}\right)$

such that:

$(1): \quad c_1 + c_2 + \cdots + c_k = n$
$(2): \quad \forall i \in \left[{1 \,.\,.\, k}\right]: c_i \in \Z_{> 0}$, that is, all the $c_i$ are strictly positive integers.