Identifier
Values
=>
Cc0022;cc-rep-0 Cc0014;cc-rep-1 Cc0002;cc-rep
['A',1]=>([],1)=>[2]=>3 ['A',2]=>([(0,2),(1,2)],3)=>[3,2]=>12 ['B',2]=>([(0,3),(1,3),(3,2)],4)=>[4,2]=>15 ['G',2]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>[6,2]=>21
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Description
The number of linear extensions of a certain poset defined for an integer partition.
The poset is constructed in David Speyer's answer to Matt Fayers' question [3].
The value at the partition $\lambda$ also counts cover-inclusive Dyck tilings of $\lambda\setminus\mu$, summed over all $\mu$, as noticed by Philippe Nadeau in a comment.
This statistic arises in the homogeneous Garnir relations for the universal graded Specht modules for cyclotomic quiver Hecke algebras.
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.