Definition:Composition


 * Set Theory:
 * Composition of Mappings or Relations: $\mathcal R_2 \circ \mathcal R_1 = \left\{{\left({x, z}\right): x \in S_1, z \in S_3: \exists y \in S_2: \left({x, y}\right) \in \mathcal R_1 \land \left({y, z}\right) \in \mathcal R_2}\right\}$


 * Abstract Algebra:
 * Another word for an operation, usually binary.


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