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Definition & Example
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- A **skew partition** $(\lambda,\mu)$ of $n \in \mathbb{N}_+$ is a pair of [integer partitions](/IntegerPartitions) such that $\mu \subseteq \lambda$ as Ferrers diagrams.
- Skew partitions are graphically represented by their [Ferrers](http://en.wikipedia.org/wiki/Norman_Macleod_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 $n$.
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- The number of skew partitions is [A225114](http://oeis.org/A225114).
Properties
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TBA
References
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Sage examples
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{{{#!sagecell
for n in [2,3,4,5]:
print SkewPartitions(n).cardinality()
for c in SkewPartitions(3):
print c
}}}
Technical information for database usage
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- A skew partition is uniquely represented as a list of pairs representing the two [integer partitions](/IntegerPartitions).
- 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.