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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.

Properties

TBA

References

Sage examples

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.