Identifier
Values
['A',1] => ([],1) => [2] => 1
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 4
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 9
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Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even.
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even.
This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1].
The case of an odd minimum is St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd..
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.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.