# Definition:Composition (Combinatorics)

A $k$-composition of a (strictly) positive integer $n \in \Z_{> 0}$ is an ordered $k$-tuple:
$c = \left({c_1, c_2, \ldots, c_k}\right)$
$(1): \quad c_1 + c_2 + \cdots + c_k = n$
$(2): \quad \forall i \in \left[{1 \,.\,.\, k}\right]: c_i \in \Z_{> 0}$, that is, all the $c_i$ are strictly positive integers.