Identifier
Values
{{1,3},{2}} => [3,2,1] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 2
{{1},{2,3}} => [1,3,2] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 2
{{1},{2},{3}} => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 2
{{1,4},{2,3}} => [4,3,2,1] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
{{1},{2,4},{3}} => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 3
{{1},{2},{3,4}} => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 3
{{1},{2},{3},{4}} => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 3
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.