Identifier
Values
([(0,2),(1,2)],3) => [1,1] => [1,1,0,0] => 1
([(0,1),(0,2),(1,2)],3) => [3] => [1,0,1,0,1,0] => 0
([(1,3),(2,3)],4) => [1,1] => [1,1,0,0] => 1
([(0,3),(1,3),(2,3)],4) => [1,1,1] => [1,1,0,1,0,0] => 2
([(0,3),(1,2)],4) => [1,1] => [1,1,0,0] => 1
([(0,3),(1,2),(2,3)],4) => [1,1,1] => [1,1,0,1,0,0] => 2
([(1,2),(1,3),(2,3)],4) => [3] => [1,0,1,0,1,0] => 0
([(0,3),(1,2),(1,3),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(2,4),(3,4)],5) => [1,1] => [1,1,0,0] => 1
([(1,4),(2,4),(3,4)],5) => [1,1,1] => [1,1,0,1,0,0] => 2
([(0,4),(1,4),(2,4),(3,4)],5) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,4),(2,3)],5) => [1,1] => [1,1,0,0] => 1
([(1,4),(2,3),(3,4)],5) => [1,1,1] => [1,1,0,1,0,0] => 2
([(0,1),(2,4),(3,4)],5) => [1,1,1] => [1,1,0,1,0,0] => 2
([(2,3),(2,4),(3,4)],5) => [3] => [1,0,1,0,1,0] => 0
([(0,4),(1,4),(2,3),(3,4)],5) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,4),(2,3),(2,4),(3,4)],5) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(1,3),(1,4),(2,3),(2,4)],5) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(3,5),(4,5)],6) => [1,1] => [1,1,0,0] => 1
([(2,5),(3,5),(4,5)],6) => [1,1,1] => [1,1,0,1,0,0] => 2
([(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(2,5),(3,4)],6) => [1,1] => [1,1,0,0] => 1
([(2,5),(3,4),(4,5)],6) => [1,1,1] => [1,1,0,1,0,0] => 2
([(1,2),(3,5),(4,5)],6) => [1,1,1] => [1,1,0,1,0,0] => 2
([(3,4),(3,5),(4,5)],6) => [3] => [1,0,1,0,1,0] => 0
([(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(0,1),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(2,5),(3,4),(3,5),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(2,4),(2,5),(3,4),(3,5)],6) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,5),(1,5),(2,4),(3,4)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [1,1,0,1,0,0] => 2
([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(0,1),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(4,6),(5,6)],7) => [1,1] => [1,1,0,0] => 1
([(3,6),(4,6),(5,6)],7) => [1,1,1] => [1,1,0,1,0,0] => 2
([(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(3,6),(4,5)],7) => [1,1] => [1,1,0,0] => 1
([(3,6),(4,5),(5,6)],7) => [1,1,1] => [1,1,0,1,0,0] => 2
([(2,3),(4,6),(5,6)],7) => [1,1,1] => [1,1,0,1,0,0] => 2
([(4,5),(4,6),(5,6)],7) => [3] => [1,0,1,0,1,0] => 0
([(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,2),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(3,6),(4,5),(4,6),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(3,5),(3,6),(4,5),(4,6)],7) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [1,1,0,1,0,0] => 2
([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(1,2),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
([(0,3),(1,2),(4,6),(5,6)],7) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
>>> Load all 128 entries. <<<
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
search for individual values
searching the database for the individual values of this statistic
Description
Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
The modified algebra B is obtained from the stable Auslander algebra kQ/I by deleting all relations which contain walks of length at least three (conjectural this step of deletion is not necessary as the stable higher Auslander algebras might be quadratic) and taking as B then the algebra kQ^(op)/J when J is the quadratic perp of the ideal I.
See www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.
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 edge-partition of biconnected components
Description
Sends a graph to the partition recording the number of edges in its biconnected components.
The biconnected components are also known as blocks of a graph.