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# 1. Definition & Example

A

**skew partition**$(\lambda,\mu)$ of $n \in \mathbb{N}_+$ is a pair of integer partitions such that $\mu \subseteq \lambda$ as Ferrers diagrams.Skew partitions are graphically represented by their Ferrers diagram (or Young diagram) as the collection of boxes of $\lambda$ that are not boxes of $\mu$.

A skew partition is

**reduced**if its Ferrers diagram does not contain empty rows before the last nonempty row and empty columns before the last nonempty column.We write $(\lambda,\mu) \vdash n$ if $\lambda$ is a partition of $n$.

the 9 Skew partitions of size 3 | ||||||||

[[3],[]] |
[[2,1],[]] |
[[3,1],[1]] |
[[2,2],[1]] |
[[3,2],[2]] |
[[1,1,1],[]] |
[[2,2,1],[1,1]] |
[[2,1,1],[1]] |
[[3,2,1],[2,1]] |

The number of skew partitions is A225114.

# 2. Properties

TBA

# 3. References

# 4. Sage examples

# 5. Technical information for database usage

A skew partition is uniquely represented as a list of pairs representing the two integer partitions.

- Skew partitions are graded by the size of the bigger partition minus the size of the smaller one.
- The database contains all integer partitions of size at most 7.