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Identifier
Values
['A',1] => ([],1) => [1] => [1,0] => 1
['A',2] => ([(0,2),(1,2)],3) => [2,1] => [1,0,1,1,0,0] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
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Description
The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
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 α≺β if β−α is a simple root.
Map
Greene-Kleitman invariant
Description
The Greene-Kleitman invariant of a poset.
This is the partition (c1−c0,c2−c1,c3−c2,…), where ck is the maximum cardinality of a union of k chains of the poset. Equivalently, this is the conjugate of the partition (a1−a0,a2−a1,a3−a2,…), where ak is the maximum cardinality of a union of k antichains of the poset.