Identifier
Values
['A',1] => ([],1) => [1] => [[1],[]] => 1
['A',2] => ([(0,2),(1,2)],3) => [2,1] => [[2,1],[]] => 3
['B',2] => ([(0,3),(1,3),(3,2)],4) => [3,1] => [[3,1],[]] => 3
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Description
The number of corners of a skew partition.
This is also known as the number of removable cells of the skew partition.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
Greene-Kleitman invariant
Description
The Greene-Kleitman invariant of a poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.