Possible database queries for integer compositions: search your data / browse all statistics / browse all maps
1. Definition & Example
An integer composition $\alpha$ of $n \in \mathbb{N}_+$ is a sequence $\alpha = (\alpha_1,\ldots,\alpha_k)$ such that $\alpha_i \in \mathbb{N}_{+}$ and $\sum_{1 \leq i \leq k} \alpha_i = n$.
The four integer compositions of $3$ |
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[1,1,1] |
[1,2] |
[2,1] |
[3] |
There are $2^{n-1}$ integer compositions of $n$,n, see A000079, and $\binom{n-1}{k}$ integer compositions of $n$ into $k$ parts, see A007318.
2. Additional information
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3. References
4. Sage examples
5. Technical information for database usage
An integer composition is uniquely represented as a list of its parts.
Integer compositions are graded by their sum.
- The database contains all integer compositions of size at most 10.