Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001348
Mapping
St001348: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 2
[1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => 3
[1,0,1,1,0,0]
 => 4
[1,1,0,0,1,0]
 => 3
[1,1,0,1,0,0]
 => 3
[1,1,1,0,0,0]
 => 3
[1,0,1,0,1,0,1,0]
 => 4
[1,0,1,0,1,1,0,0]
 => 5
[1,0,1,1,0,0,1,0]
 => 6
[1,0,1,1,0,1,0,0]
 => 6
[1,0,1,1,1,0,0,0]
 => 5
[1,1,0,0,1,0,1,0]
 => 4
[1,1,0,0,1,1,0,0]
 => 5
[1,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => 4
[1,1,0,1,1,0,0,0]
 => 4
[1,1,1,0,0,0,1,0]
 => 4
[1,1,1,0,0,1,0,0]
 => 5
[1,1,1,0,1,0,0,0]
 => 4
[1,1,1,1,0,0,0,0]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => 5
[1,0,1,0,1,0,1,1,0,0]
 => 6
[1,0,1,0,1,1,0,0,1,0]
 => 7
[1,0,1,0,1,1,0,1,0,0]
 => 7
[1,0,1,0,1,1,1,0,0,0]
 => 6
[1,0,1,1,0,0,1,0,1,0]
 => 8
[1,0,1,1,0,0,1,1,0,0]
 => 9
[1,0,1,1,0,1,0,0,1,0]
 => 8
[1,0,1,1,0,1,0,1,0,0]
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => 8
[1,0,1,1,1,0,0,0,1,0]
 => 7
[1,0,1,1,1,0,0,1,0,0]
 => 7
[1,0,1,1,1,0,1,0,0,0]
 => 6
[1,0,1,1,1,1,0,0,0,0]
 => 7
[1,1,0,0,1,0,1,0,1,0]
 => 5
[1,1,0,0,1,0,1,1,0,0]
 => 6
[1,1,0,0,1,1,0,0,1,0]
 => 7
[1,1,0,0,1,1,0,1,0,0]
 => 7
[1,1,0,0,1,1,1,0,0,0]
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => 5
[1,1,0,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,1,0,0,1,0]
 => 5
[1,1,0,1,0,1,0,1,0,0]
 => 5
[1,1,0,1,0,1,1,0,0,0]
 => 5
[1,1,0,1,1,0,0,0,1,0]
 => 5
[1,1,0,1,1,0,0,1,0,0]
 => 6
[1,1,0,1,1,0,1,0,0,0]
 => 5
[1,1,0,1,1,1,0,0,0,0]
 => 5
Description
The bounce of the parallelogram polyomino associated with the Dyck path. A bijection due to Delest and Viennot [1] associates a Dyck path with a parallelogram polyomino. The bounce statistic is defined in [2].
Matching statistic: St001880
(load all 4 compositions to match this statistic)
Mapping
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Values
[1,0]
 => [1,0]
 => [.,.]
 => ([],1)
 => ? = 1
[1,0,1,0]
 => [1,1,0,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 2
[1,1,0,0]
 => [1,0,1,0]
 => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 2
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 4
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 5
[1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6
[1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6
[1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 5
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 5
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 5
[1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 9
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 7
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[[[[.,.],.],.],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 7
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [[[[.,.],.],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 8
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [[[[.,.],.],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 8
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [[[[[.,.],.],.],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 7
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[[.,.],.],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 10
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,[.,.]],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [[[[.,.],.],[[.,.],.]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 8
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[[[.,.],.],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 8
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [[[[[.,.],.],[.,.]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 7
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[[[.,.],.],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 8
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [[.,.],[[[[.,.],.],.],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 10
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,1,0,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001879
(load all 4 compositions to match this statistic)
Mapping
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 25%
Values
[1,0]
 => [1,0]
 => [.,.]
 => ([],1)
 => ? = 1 - 1
[1,0,1,0]
 => [1,1,0,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 2 - 1
[1,1,0,0]
 => [1,0,1,0]
 => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 2 - 1
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 4 - 1
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 5 - 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 1
[1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 5 - 1
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 5 - 1
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [.,[[.,[.,.]],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [[.,[[.,.],.]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 5 - 1
[1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6 - 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7 - 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7 - 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6 - 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8 - 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 9 - 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8 - 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8 - 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[.,.],[[.,[.,.]],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 8 - 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7 - 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 7 - 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6 - 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7 - 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7 - 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 7 - 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6 - 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[[.,[.,.]],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [.,[[.,[[.,.],.]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6 - 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [.,[[[.,[.,.]],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [.,[[.,[.,[.,.]]],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [[.,[[[.,.],.],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7 - 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 7 - 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6 - 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6 - 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6 - 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [[.,[.,[[.,.],.]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 6 - 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [[.,[[.,[.,.]],.]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 5 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[[[[.,.],.],.],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 7 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [[[[.,.],.],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 8 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [[[[.,.],.],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 8 - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [[[[[.,.],.],.],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[[.,.],.],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 10 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9 - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,[.,.]],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 9 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [[[[.,.],.],[[.,.],.]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 8 - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[[[.,.],.],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 8 - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [[[[[.,.],.],[.,.]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 7 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[[[.,.],.],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 8 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [[.,.],[[[[.,.],.],.],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 10 - 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[[.,[.,.]],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [.,[.,[[.,[[.,.],.]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[[[.,[.,.]],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[[.,[.,[.,.]]],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [.,[[.,[[[.,.],.],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [.,[[[.,[[.,.],.]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [.,[[[[.,[.,.]],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [.,[[.,[.,[[.,.],.]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [.,[[.,[[.,[.,.]],.]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[[.,[.,[.,[.,.]]]],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [.,[[[.,[.,[.,.]]],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [[.,[[[[.,.],.],.],.]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,1,0,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 1
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [[.,[.,[[[.,.],.],.]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 6 - 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.