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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.

TBA

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.