Definition:Composition


 * Set Theory: Composition of Mappings or Relations: $$\mathcal R_2 \circ \mathcal R_1 = \left\{{\left({x, z}\right): x \in S_1, z \in S_3: \exists y \in S_2: \left({x, y}\right) \in \mathcal R_1 \and \left({y, z}\right) \in \mathcal R_2}\right\}$$.
 * Abstract Algebra: Another word for an operation, usually binary.
 * Combinatorics: a $k$-composition of a positive integer $$n \in \Z: n > 0$$ 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 $$c_i \in \Z: c_i > 0$$ for all $$i$$.