Identifier
Values
([(0,1),(0,2),(1,2)],3) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,3),(1,3),(2,3)],4) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,3),(1,2),(2,3)],4) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(1,2),(1,3),(2,3)],4) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,4),(2,4),(3,4)],5) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,4),(1,4),(2,4),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,4),(2,3),(3,4)],5) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,1),(2,4),(3,4)],5) => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
([(2,3),(2,4),(3,4)],5) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(0,4),(1,4),(2,3),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,4),(2,3),(2,4),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,3),(1,4),(2,3),(2,4)],5) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(1,3),(2,3),(2,4)],5) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,5),(3,5),(4,5)],6) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(1,5),(2,5),(3,5),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,5),(3,4),(4,5)],6) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(1,2),(3,5),(4,5)],6) => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
([(3,4),(3,5),(4,5)],6) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(1,5),(2,5),(3,4),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,1),(2,5),(3,5),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(2,5),(3,4),(3,5),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,4),(2,5),(3,4),(3,5)],6) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
([(1,5),(2,4),(3,4),(3,5)],6) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(0,1),(2,5),(3,4),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
([(3,6),(4,6),(5,6)],7) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(2,6),(3,6),(4,6),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(3,6),(4,5),(5,6)],7) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(2,3),(4,6),(5,6)],7) => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
([(4,5),(4,6),(5,6)],7) => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1
([(2,6),(3,6),(4,5),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,2),(3,6),(4,6),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(3,6),(4,5),(4,6),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(3,5),(3,6),(4,5),(4,6)],7) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
([(2,6),(3,5),(4,5),(4,6)],7) => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
([(1,2),(3,6),(4,5),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 0
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,0] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
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
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
Map
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.