Identifier
Values
['A',1] => ([],1) => [2] => [1,1] => 0
['A',2] => ([(0,2),(1,2)],3) => [3,2] => [2,2,1] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => [2,2,1,1] => 0
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => [2,2,1,1,1,1] => 0
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Description
The minimal difference in size when partitioning the integer partition into two subpartitions.
This is the optimal value of the optimisation version of the partition problem [1].
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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.
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conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.