Identifier
-
Mp00253:
Decorated permutations
—permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤ
Values
[+,+,+] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[-,+,+] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[+,-,+] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[+,+,-] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[-,-,+] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[-,+,-] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[+,-,-] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[-,-,-] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 3
[+,3,2] => [1,3,2] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 3
[-,3,2] => [1,3,2] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 3
[3,1,2] => [3,1,2] => [[.,[.,.]],.] => ([(0,2),(2,1)],3) => 3
[3,+,1] => [3,2,1] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 3
[3,-,1] => [3,2,1] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 3
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[+,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[-,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,+,2] => [4,1,3,2] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => 4
[4,1,-,2] => [4,1,3,2] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => 4
[4,3,1,2] => [4,3,1,2] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => 4
[4,3,2,1] => [4,3,2,1] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,5,3,4] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,5,+,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,5,+,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,5,+,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,5,-,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,5,+,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,5,-,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,5,-,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,5,-,3] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,5,2,3,4] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,5,2,+,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,5,2,+,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,5,2,-,3] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
>>> Load all 284 entries. <<<
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searching the database for the individual values of this statistic
Description
The number of 2-Gorenstein indecomposable injective modules 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
permutation
Description
The underlying permutation of the decorated permutation.
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