Composition of an integer

Definition

Let $n$ be a natural number. A composition of $n$ is a finite sequence $(a_1, \dots, a_k)$ of positive integers with $a_1 + \dots + a_k = n$ . The number $k$ is the number of parts of the composition.

Remarks

Unlike a partition, a composition records the order of its parts. The compositions of $3$ are $(3)$ , $(2, 1)$ , $(1, 2)$ and $(1, 1, 1)$ . The number $0$ has exactly one composition, the empty sequence.

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Number of compositions

Tag	`0J8ANSYKAC`
URI	`m2://0J8ANSYKAC`
Kind	definition
Writing	W0 stub
MSC	05A17
Defines	Composition of an integer

Composition of an integer

Definition

Remarks

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