\begin{definition}[Definition:Composition (Combinatorics)]
A $k$-composition of a (strictly) positive integer $n \in \Z_{> 0}$ is an ordered $k$-tuple:
:$c = \tuple {c_1, c_2, \ldots, c_k}$
such that:
:$(1): \quad c_1 + c_2 + \cdots + c_k = n$
:$(2): \quad \forall i \in \closedint 1 k: c_i \in \Z_{>0}$, that is, all the $c_i$ are strictly positive integers.
Category:Definitions/Combinatorics
\end{definition}