Identifier
Values
[.,[.,[.,.]]] => [3,2,1] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 2
[[.,.],[.,.]] => [1,3,2] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 2
[[[.,.],.],.] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 2
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
[[.,.],[.,[.,.]]] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 3
[[[.,.],.],[.,.]] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 3
[[[[.,.],.],.],.] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 3
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[[.,.],.],.],.],.],[.,.]] => [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] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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
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 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.