Identifier
Values
([(0,1)],2) => [1] => [1,0] => 0
([(1,2)],3) => [1] => [1,0] => 0
([(0,2),(1,2)],3) => [2] => [1,0,1,0] => 0
([(0,1),(0,2),(1,2)],3) => [3] => [1,0,1,0,1,0] => 0
([(2,3)],4) => [1] => [1,0] => 0
([(1,3),(2,3)],4) => [2] => [1,0,1,0] => 0
([(0,3),(1,3),(2,3)],4) => [3] => [1,0,1,0,1,0] => 0
([(0,3),(1,2)],4) => [1,1] => [1,1,0,0] => 1
([(0,3),(1,2),(2,3)],4) => [3] => [1,0,1,0,1,0] => 0
([(1,2),(1,3),(2,3)],4) => [3] => [1,0,1,0,1,0] => 0
([(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
([(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
([(3,4)],5) => [1] => [1,0] => 0
([(2,4),(3,4)],5) => [2] => [1,0,1,0] => 0
([(1,4),(2,4),(3,4)],5) => [3] => [1,0,1,0,1,0] => 0
([(0,4),(1,4),(2,4),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,4),(2,3)],5) => [1,1] => [1,1,0,0] => 1
([(1,4),(2,3),(3,4)],5) => [3] => [1,0,1,0,1,0] => 0
([(0,1),(2,4),(3,4)],5) => [2,1] => [1,0,1,1,0,0] => 1
([(2,3),(2,4),(3,4)],5) => [3] => [1,0,1,0,1,0] => 0
([(0,4),(1,4),(2,3),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,4),(2,3),(2,4),(3,4)],5) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,4),(1,3),(2,3),(2,4)],5) => [4] => [1,0,1,0,1,0,1,0] => 0
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(4,5)],6) => [1] => [1,0] => 0
([(3,5),(4,5)],6) => [2] => [1,0,1,0] => 0
([(2,5),(3,5),(4,5)],6) => [3] => [1,0,1,0,1,0] => 0
([(1,5),(2,5),(3,5),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(2,5),(3,4)],6) => [1,1] => [1,1,0,0] => 1
([(2,5),(3,4),(4,5)],6) => [3] => [1,0,1,0,1,0] => 0
([(1,2),(3,5),(4,5)],6) => [2,1] => [1,0,1,1,0,0] => 1
([(3,4),(3,5),(4,5)],6) => [3] => [1,0,1,0,1,0] => 0
([(1,5),(2,5),(3,4),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,1),(2,5),(3,5),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(2,5),(3,4),(3,5),(4,5)],6) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [2,2] => [1,1,1,0,0,0] => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5] => [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) => [4] => [1,0,1,0,1,0,1,0] => 0
([(0,1),(2,5),(3,4),(4,5)],6) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [3,2] => [1,0,1,1,1,0,0,0] => 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
([(5,6)],7) => [1] => [1,0] => 0
([(4,6),(5,6)],7) => [2] => [1,0,1,0] => 0
([(3,6),(4,6),(5,6)],7) => [3] => [1,0,1,0,1,0] => 0
([(2,6),(3,6),(4,6),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(3,6),(4,5)],7) => [1,1] => [1,1,0,0] => 1
([(3,6),(4,5),(5,6)],7) => [3] => [1,0,1,0,1,0] => 0
([(2,3),(4,6),(5,6)],7) => [2,1] => [1,0,1,1,0,0] => 1
([(4,5),(4,6),(5,6)],7) => [3] => [1,0,1,0,1,0] => 0
([(2,6),(3,6),(4,5),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,2),(3,6),(4,6),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(3,6),(4,5),(4,6),(5,6)],7) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [2,2] => [1,1,1,0,0,0] => 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [3,2] => [1,0,1,1,1,0,0,0] => 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [5] => [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) => [4] => [1,0,1,0,1,0,1,0] => 0
([(1,2),(3,6),(4,5),(5,6)],7) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
([(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) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([(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) => [3,2] => [1,0,1,1,1,0,0,0] => 1
>>> Load all 111 entries. <<<
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2] => [1,0,1,1,1,0,0,0] => 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
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [1,1,1,0,1,0,0,0] => 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
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 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] => 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [1,1,1,0,1,0,0,0] => 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
([(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
The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path.
The statistic returns zero in case that bimodule is the zero module.
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 connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.