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 $3$ [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. FindStat representation and coverage

• 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.