Identifier
Values
['A',1] => ([],1) => [2] => 2
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 4
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 5
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 7
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Description
The product of the hook lengths of the diagonal cells in an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the product of the hook lengths of the diagonal cells $(i,i)$ of a partition.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a 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.