1. (relative product) A method of combining functions in a serial manner. The composition of two functions
is the function
with the property that
This is usually written as
g °
f. The process of performing composition is an operation between functions of suitable kinds. It is associative, and identity functions fulfil the role of units.
If R denotes the set of real numbers and
then
f°
g is the function
h:
The idea of composition of functions can be extended to functions of several variables.
2. A subdivision of a positive integer n into parts a1, a2,… ak in which the ordering is significant and in which
where each
ai is a positive integer. It is thus similar to a partition (
see covering) but in a partition the ordering is not significant. In general the number of compositions of
n is 2
n−1.
3. A particular form of association between entities found in object-oriented approaches. The association is used to indicate a hierarchy of objects such that objects lower in the hierarchy are part of objects higher in the hierarchy. Thus the hierarchy indicates a component structure.