<> Definition & Example ==================== - 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 $n$. <> - The number of skew partitions is [A225114](http://oeis.org/A225114). Properties ========== TBA References ========== <> Sage examples ============= {{{#!sagecell for n in [2,3,4,5]: print SkewPartitions(n).cardinality() for c in SkewPartitions(3): print c }}} Technical information for database usage ======================================== - 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.