Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000727
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000727: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => [1,0,1,0]
 => [2,1] => [1,2] => 2
[2]
 => [1,1,0,0,1,0]
 => [3,1,2] => [1,2,3] => 3
[1,1]
 => [1,0,1,1,0,0]
 => [2,3,1] => [1,2,3] => 3
[3]
 => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [1,2,3,4] => 4
[2,1]
 => [1,0,1,0,1,0]
 => [3,2,1] => [1,2,3] => 3
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [1,2,3,4] => 4
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => [1,2,3,4,5] => 5
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => [1,3,2,4] => 4
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [1,2,3,4] => 4
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => [1,2,4,3] => 3
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [1,2,3,4,5] => 5
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [6,1,2,3,4,5] => [1,2,3,4,5,6] => 6
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => [1,3,4,2,5] => 5
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => [1,2,3,4] => 4
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => [1,2,3,4] => 4
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => [1,2,3,4] => 4
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => [1,2,4,5,3] => 5
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 6
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => 7
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [6,2,1,3,4,5] => [1,3,4,5,2,6] => 6
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,2,4] => [1,2,4,3,5] => 5
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => [1,4,2,3,5] => 5
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [1,2,3,4,5] => 5
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => [1,2,3,4] => 4
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => [1,2,3,5,4] => 4
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [1,2,3,4,5] => 5
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => [1,2,5,3,4] => 4
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => [1,2,4,5,6,3] => 6
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => 7
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [7,2,1,3,4,5,6] => [1,3,4,5,6,2,7] => 7
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [6,3,1,2,4,5] => [1,2,4,5,3,6] => 6
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [6,2,3,1,4,5] => [1,4,5,2,3,6] => 6
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => [1,2,3,4,5] => 5
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => [1,4,2,3,5] => 5
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => [1,2,3,4,5] => 5
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => [1,3,2,4,5] => 5
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => [1,2,3,5,4] => 4
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => [1,2,5,3,4] => 4
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [4,2,3,5,6,1] => [1,2,3,5,6,4] => 6
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => [1,2,3,4,5] => 5
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [3,4,2,5,6,1] => [1,2,5,6,3,4] => 6
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => 7
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => 7
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [7,2,3,1,4,5,6] => [1,4,5,6,2,3,7] => 7
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => [1,2,3,5,4,6] => 6
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [6,3,2,1,4,5] => [1,4,5,2,3,6] => 6
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [6,2,3,4,1,5] => [1,5,2,3,4,6] => 6
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [5,6,1,2,3,4] => [1,2,3,4,5,6] => 6
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => [1,3,2,4,5] => 5
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => [1,2,3,4,5] => 5
Description
The largest label of a leaf in the binary search tree associated with the permutation. Alternatively, this is 1 plus the position of the last descent of the inverse of the reversal of the permutation, and 1 if there is no descent.
Matching statistic: St001880
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 83%
Values
[1]
 => [1,0,1,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 2
[2]
 => [1,1,0,0,1,0]
 => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 3
[1,1]
 => [1,0,1,1,0,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 3
[3]
 => [1,1,1,0,0,0,1,0]
 => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[2,1]
 => [1,0,1,0,1,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 4
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 5
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 4
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [[.,.],[.,[.,[[.,.],.]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[[.,.],.]]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [[.,[.,[[.,.],[.,.]]]],.]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 6
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [[.,.],[.,[[.,[.,.]],.]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 5
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 6
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[[.,.],.]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,[.,.]],.]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],[.,.]]]]],.]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 7
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[.,.]]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[[.,.],[.,[.,.]]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [[.,.],[[.,[.,[.,.]]],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 5
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [[.,.],[.,[[[.,.],.],.]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [[.,.],[.,[.,[[.,[.,.]],.]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 6
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 5
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [[.,.],[.,[.,[[.,.],[.,.]]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
 => ? = 7
[6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,[.,.]]],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[[.,.],.],.]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[.,.],.]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[.,[[.,[.,.]],[.,.]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6
[5,2,1,1]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[[.,.],[[.,.],.]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6
[5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [[[.,.],[.,[.,[.,.]]]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 6
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5
[4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5
[4,2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [[.,.],[[.,[[.,.],.]],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5
[4,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [[.,.],[.,[[.,[.,[.,.]]],.]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 6
[3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5
[6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[.,[.,.]]]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[[.,.],.]],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4,1]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[.,.]],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[6,5]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[[.,.],.]]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,3,2]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [[.,[.,[[[.,[.,.]],.],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[6,5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,2]
 => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[.,[.,.]],.]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4,3]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[6,5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,3]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[.,[.,.]]],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,2,1]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[[.,.],.],.]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,3,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[[.,.],.]],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[6,5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
[6,4,3,2]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => [[.,[[[[.,[.,.]],.],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001879
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 83%
Values
[1]
 => [1,0,1,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 2 - 1
[2]
 => [1,1,0,0,1,0]
 => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,1]
 => [1,0,1,1,0,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 3 - 1
[3]
 => [1,1,1,0,0,0,1,0]
 => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[2,1]
 => [1,0,1,0,1,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4 - 1
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4 - 1
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 - 1
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 4 - 1
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 4 - 1
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],.]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5 - 1
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 - 1
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 5 - 1
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 4 - 1
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [[.,.],[.,[.,[[.,.],.]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7 - 1
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[.,[[.,.],.]]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,.]],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [[.,[.,[[.,.],[.,.]]]],.]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 6 - 1
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 - 1
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 - 1
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 - 1
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [[.,.],[.,[[.,[.,.]],.]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 5 - 1
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 6 - 1
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [[.,.],[.,[.,[.,[[.,.],.]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7 - 1
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,[.,.]],.]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],[.,.]]]]],.]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 7 - 1
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[.,.]]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[[.,.],[.,[.,.]]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 - 1
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 - 1
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 - 1
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [[.,.],[[.,[.,[.,.]]],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5 - 1
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 5 - 1
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 4 - 1
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [[.,.],[.,[[[.,.],.],.]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [[.,.],[.,[.,[[.,[.,.]],.]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7 - 1
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 6 - 1
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 5 - 1
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [[.,.],[.,[.,[[.,.],[.,.]]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
 => ? = 7 - 1
[6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,[.,.]]],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [[.,[.,[.,[[[.,.],.],.]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[.,.],.]],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[.,[[.,[.,.]],[.,.]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 - 1
[5,2,1,1]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[[.,.],[[.,.],.]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 - 1
[5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [[[.,.],[.,[.,[.,.]]]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 6 - 1
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 6 - 1
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5 - 1
[4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 - 1
[4,2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [[.,.],[[.,[[.,.],.]],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5 - 1
[4,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [[.,.],[.,[[.,[.,[.,.]]],.]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 7 - 1
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 6 - 1
[3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 5 - 1
[6,4]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[.,[.,.]]]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,3,1]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[[.,.],.]],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4,1]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,3,2]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[.,.]],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[6,5]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,1]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [[.,[[.,[.,[[.,.],.]]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,3,2]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [[.,[.,[[[.,[.,.]],.],.]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,3,2,1]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[6,5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,2]
 => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[.,[.,.]],.]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4,3]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[5,4,2,1]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[6,5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,3]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[.,[.,.]]],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,2,1]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => [[.,[[.,[[[.,.],.],.]],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4,3,1]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,3,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => [[.,[[[.,[[.,.],.]],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[6,5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
[6,4,3,2]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => [[.,[[[[.,[.,.]],.],.],.]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 7 - 1
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.