Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000681
Mapping
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0,1,0]
 => [2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,1,0,0,1,0]
 => [3,1] => [[3,3],[2]]
 => [2]
 => 1
[1,1,1,0,0,0,1,0]
 => [3,1] => [[3,3],[2]]
 => [2]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,2] => [[4,3],[2]]
 => [2]
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 2
[1,1,0,1,1,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,2] => [[4,3],[2]]
 => [2]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => [[3,3,1,1],[2]]
 => [2]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,3,1] => [[3,3,1,1],[2]]
 => [2]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 2
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => [2,1]
 => 0
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => 2
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,2] => [[4,3,1],[2]]
 => [2]
 => 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 2
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => 2
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,3,2] => [[4,3,1],[2]]
 => [2]
 => 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 2
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 2
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 2
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => 0
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,2,2] => [[4,3,2],[2,1]]
 => [2,1]
 => 0
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,3,1] => [[4,4,2],[3,1]]
 => [3,1]
 => 3
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,3,1] => [[4,4,2],[3,1]]
 => [3,1]
 => 3
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => 4
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [3,1,2] => [[4,3,3],[2,2]]
 => [2,2]
 => 2
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [3,2,1] => [[4,4,3],[3,2]]
 => [3,2]
 => 0
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [3,3] => [[5,3],[2]]
 => [2]
 => 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [3,3] => [[5,3],[2]]
 => [2]
 => 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [4,1,1] => [[4,4,4],[3,3]]
 => [3,3]
 => 4
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [4,2] => [[5,4],[3]]
 => [3]
 => 2
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [5,1] => [[5,5],[4]]
 => [4]
 => 3
Description
The Grundy value of Chomp on Ferrers diagrams. Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1]. This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
Mapping
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 40%
Values
[1,1,0,0,1,0,1,0]
 => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 2
[1,1,0,1,0,0,1,0]
 => [[.,[.,.]],[.,.]]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 1 + 2
[1,1,1,0,0,0,1,0]
 => [[[.,.],.],[.,.]]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 1 + 2
[1,0,1,1,0,0,1,0,1,0]
 => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,0,1,0,0,1,0]
 => [.,[[.,[.,.]],[.,.]]]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,1,0,0,0,1,0]
 => [.,[[[.,.],.],[.,.]]]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,1,0,0,1,0]
 => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 0 + 2
[1,1,0,1,0,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 1 + 2
[1,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,.]]],[.,.]]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 2 + 2
[1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],.]],[.,.]]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 2 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 1 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [[[.,[.,.]],.],[.,.]]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 2 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [[[[.,.],.],.],[.,.]]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 2 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [.,[.,[[.,[.,.]],[.,.]]]]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [.,[.,[[[.,.],.],[.,.]]]]
 => [[.,.],[[[.,.],.],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [.,[[.,.],[.,[[.,.],.]]]]
 => [[.,[.,.]],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [.,[[.,[.,.]],[[.,.],.]]]
 => [[.,[.,[.,.]]],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [.,[[.,[.,[.,.]]],[.,.]]]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [.,[[.,[[.,.],.]],[.,.]]]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 2
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [.,[[[.,.],.],[[.,.],.]]]
 => [[.,[[.,.],.]],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 2
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [.,[[[.,[.,.]],.],[.,.]]]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 2
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [.,[[[[.,.],.],.],[.,.]]]
 => [[.,[[[.,.],.],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 2
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [[.,.],[.,[.,[[.,.],.]]]]
 => [[[.,.],.],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => [[[.,.],.],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [[.,.],[.,[[.,[.,.]],.]]]
 => [[[.,.],.],[[.,[.,.]],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [[.,.],[.,[[[.,.],.],.]]]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => [[[.,.],[.,.]],[.,[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [[.,.],[[.,.],[[.,.],.]]]
 => [[[.,.],[.,.]],[[.,.],.]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => [[[.,.],[.,[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[.,.],[[[.,.],.],[.,.]]]
 => [[[.,.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => [[[.,[.,.]],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 2
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [[.,[.,.]],[.,[[.,.],.]]]
 => [[[.,[.,.]],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => [[[.,[.,.]],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 0 + 2
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [[.,[.,.]],[[.,[.,.]],.]]
 => [[[.,[.,.]],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 2
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [[.,[.,.]],[[[.,.],.],.]]
 => [[[.,[.,.]],[[.,.],.]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 2
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => [[[.,[.,[.,.]]],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 4 + 2
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [[.,[.,[.,.]]],[[.,.],.]]
 => [[[.,[.,[.,.]]],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 2 + 2
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => [[[.,[[.,.],.]],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 4 + 2
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [[.,[[.,.],.]],[[.,.],.]]
 => [[[.,[[.,.],.]],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 2 + 2
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => [[[.,[[.,.],[.,.]]],.],.]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 3 + 2
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[[[.,.],.],.]],[.,.]]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => [[[[.,.],.],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 2
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,[[.,.],.]]]
 => [[[[.,.],.],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [[[.,.],.],[[.,.],[.,.]]]
 => [[[[.,.],.],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 0 + 2
[1,1,1,0,0,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,[.,.]],.]]
 => [[[[.,.],.],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 2
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [[[.,[.,[.,.]]],.],[.,.]]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [[[.,[[.,.],.]],.],[.,.]]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [[[[.,[.,.]],.],.],[.,.]]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [[[[[.,.],.],.],.],[.,.]]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 3 + 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],.]]]],[.,.]]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,.]],.]]],[.,.]]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[.,[[[.,.],.],.]]],[.,.]]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [[.,[[.,[.,[.,.]]],.]],[.,.]]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
 => [[.,[[.,[[.,.],.]],.]],[.,.]]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
 => [[.,[[[.,[.,.]],.],.]],[.,.]]
 => [[[.,[[[.,[.,.]],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [[.,[[[[.,.],.],.],.]],[.,.]]
 => [[[.,[[[[.,.],.],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [[[.,[.,[.,[.,.]]]],.],[.,.]]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [[[.,[.,[[.,.],.]]],.],[.,.]]
 => [[[[.,[.,[[.,.],.]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [[[.,[[.,[.,.]],.]],.],[.,.]]
 => [[[[.,[[.,[.,.]],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [[[.,[[[.,.],.],.]],.],[.,.]]
 => [[[[.,[[[.,.],.],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[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 = 4 + 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[[[.,[[.,.],.]],.],.],[.,.]]
 => [[[[[.,[[.,.],.]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 4 + 2
[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 = 4 + 2
[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 = 4 + 2
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.
Matching statistic: St001880
(load all 2 compositions to match this statistic)
Mapping
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 40%
Values
[1,1,0,0,1,0,1,0]
 => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 3
[1,1,0,1,0,0,1,0]
 => [[.,[.,.]],[.,.]]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[1,1,1,0,0,0,1,0]
 => [[[.,.],.],[.,.]]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,0,1,0]
 => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0]
 => [.,[[.,[.,.]],[.,.]]]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,1,0,0,0,1,0]
 => [.,[[[.,.],.],[.,.]]]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,0,0,1,0,1,1,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,1,0,0,1,0]
 => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 0 + 3
[1,1,0,1,0,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 3
[1,1,0,1,0,0,1,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => [[[.,[.,.]],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,.]]],[.,.]]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 2 + 3
[1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],.]],[.,.]]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 2 + 3
[1,1,1,0,0,0,1,0,1,0]
 => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 3
[1,1,1,0,0,0,1,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 1 + 3
[1,1,1,0,0,1,0,0,1,0]
 => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 3
[1,1,1,0,1,0,0,0,1,0]
 => [[[.,[.,.]],.],[.,.]]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 2 + 3
[1,1,1,1,0,0,0,0,1,0]
 => [[[[.,.],.],.],[.,.]]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 2 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [.,[.,[[.,[.,.]],[.,.]]]]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [.,[.,[[[.,.],.],[.,.]]]]
 => [[.,.],[[[.,.],.],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [.,[[.,.],[.,[[.,.],.]]]]
 => [[.,[.,.]],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [.,[[.,[.,.]],[[.,.],.]]]
 => [[.,[.,[.,.]]],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [.,[[.,[.,[.,.]]],[.,.]]]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [.,[[.,[[.,.],.]],[.,.]]]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [.,[[[.,.],.],[[.,.],.]]]
 => [[.,[[.,.],.]],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 3
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [.,[[[.,[.,.]],.],[.,.]]]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [.,[[[[.,.],.],.],[.,.]]]
 => [[.,[[[.,.],.],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 2 + 3
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [[.,.],[.,[.,[[.,.],.]]]]
 => [[[.,.],.],[.,[[.,.],.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => [[[.,.],.],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [[.,.],[.,[[.,[.,.]],.]]]
 => [[[.,.],.],[[.,[.,.]],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [[.,.],[.,[[[.,.],.],.]]]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 3
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => [[[.,.],[.,.]],[.,[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [[.,.],[[.,.],[[.,.],.]]]
 => [[[.,.],[.,.]],[[.,.],.]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => [[[.,.],[.,[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 3
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[.,.],[[[.,.],.],[.,.]]]
 => [[[.,.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 3
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => [[[.,[.,.]],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 3
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [[.,[.,.]],[.,[[.,.],.]]]
 => [[[.,[.,.]],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => [[[.,[.,.]],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 0 + 3
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [[.,[.,.]],[[.,[.,.]],.]]
 => [[[.,[.,.]],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 3
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [[.,[.,.]],[[[.,.],.],.]]
 => [[[.,[.,.]],[[.,.],.]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => [[[.,[.,[.,.]]],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 4 + 3
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [[.,[.,[.,.]]],[[.,.],.]]
 => [[[.,[.,[.,.]]],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 2 + 3
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => [[[.,[[.,.],.]],.],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 4 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [[.,[[.,.],.]],[[.,.],.]]
 => [[[.,[[.,.],.]],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 2 + 3
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => [[[.,[[.,.],[.,.]]],.],.]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 3 + 3
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[[[.,.],.],.]],[.,.]]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[.,.],.],[.,[.,[.,.]]]]
 => [[[[.,.],.],.],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 3
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,[[.,.],.]]]
 => [[[[.,.],.],.],[[.,.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 3
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [[[.,.],.],[[.,.],[.,.]]]
 => [[[[.,.],.],[.,.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 0 + 3
[1,1,1,0,0,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,[.,.]],.]]
 => [[[[.,.],.],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 1 + 3
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [[[.,[.,[.,.]]],.],[.,.]]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [[[.,[[.,.],.]],.],[.,.]]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [[[[.,[.,.]],.],.],[.,.]]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [[[[[.,.],.],.],.],[.,.]]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 3 + 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [[.,[.,[.,[[.,.],.]]]],[.,.]]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [[.,[.,[[.,[.,.]],.]]],[.,.]]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [[.,[.,[[[.,.],.],.]]],[.,.]]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [[.,[[.,[.,[.,.]]],.]],[.,.]]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
 => [[.,[[.,[[.,.],.]],.]],[.,.]]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
 => [[.,[[[.,[.,.]],.],.]],[.,.]]
 => [[[.,[[[.,[.,.]],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [[.,[[[[.,.],.],.],.]],[.,.]]
 => [[[.,[[[[.,.],.],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [[[.,[.,[.,[.,.]]]],.],[.,.]]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [[[.,[.,[[.,.],.]]],.],[.,.]]
 => [[[[.,[.,[[.,.],.]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [[[.,[[.,[.,.]],.]],.],[.,.]]
 => [[[[.,[[.,[.,.]],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [[[.,[[[.,.],.],.]],.],[.,.]]
 => [[[[.,[[[.,.],.],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[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 = 4 + 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [[[[.,[[.,.],.]],.],.],[.,.]]
 => [[[[[.,[[.,.],.]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 4 + 3
[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 = 4 + 3
[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 = 4 + 3
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 40%
Values
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3 = 1 + 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => ? = 1 + 2
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => ? = 2 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => ? = 2 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,2,3,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4 = 2 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4 = 2 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 1 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 2 + 2
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2 + 2
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 2
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 2 + 2
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 2 + 2
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 2 + 2
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 2
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 2
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 + 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 2
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 3 + 2
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 2
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 2
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 2
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 1 + 2
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 2
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 2
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 2
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 3 + 2
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 4 + 2
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 2 + 2
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [6,2,3,4,5,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [6,2,3,5,4,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
 => [6,2,4,3,5,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [6,2,4,5,3,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [6,2,5,4,3,1,7] => [1,6,2,3,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [6,3,2,4,5,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [6,3,2,5,4,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [6,3,4,2,5,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [6,3,4,5,2,1,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [6,3,5,4,2,1,7] => [1,6,2,3,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [6,4,3,2,5,1,7] => [1,6,2,4,3,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [6,4,3,5,2,1,7] => [1,6,2,4,5,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [6,5,3,4,2,1,7] => [1,6,2,5,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => [1,6,2,5,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001645
(load all 3 compositions to match this statistic)
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 40%
Values
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 3
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 3
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ? = 0 + 3
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 3
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 2 + 3
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5 = 2 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,4,2,6,5] => [2,4,5,3,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,3,5,4,2,6] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,3,5,2,6] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,4,5,3,2,6] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,3,5,4,6] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3,5,6,4] => [3,2,4,6,1,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3,6,5,4] => [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,5,6] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,6,5] => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,5,3,6] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,1,5,4,3,6] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [2,3,1,4,5,6] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 3
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [2,3,1,4,6,5] => [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,6] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [2,3,1,5,6,4] => [3,4,2,6,1,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,3,1,6,5,4] => [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,3,4,1,5,6] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 3
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [2,3,4,1,6,5] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [2,3,4,5,1,6] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [2,3,5,4,1,6] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 3
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [2,4,3,1,5,6] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [2,4,3,1,6,5] => [3,5,4,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 3
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,2,1,6] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 3 + 3
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [3,5,4,2,1,6] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 3 + 3
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [4,3,5,2,1,6] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 3 + 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [4,5,3,2,1,6] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 3 + 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 3 + 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,6,2,1,7] => [4,5,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [3,4,6,5,2,1,7] => [4,5,7,6,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
 => [3,5,4,6,2,1,7] => [4,6,5,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [3,5,6,4,2,1,7] => [4,6,7,5,3,2,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [3,6,5,4,2,1,7] => [4,7,6,5,3,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [4,3,5,6,2,1,7] => [5,4,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [4,3,6,5,2,1,7] => [5,4,7,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [4,5,3,6,2,1,7] => [5,6,4,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [4,5,6,3,2,1,7] => [5,6,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [4,6,5,3,2,1,7] => [5,7,6,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [5,4,3,6,2,1,7] => [6,5,4,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [5,4,6,3,2,1,7] => [6,5,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [5,6,4,3,2,1,7] => [6,7,5,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 4 + 3
Description
The pebbling number of a connected graph.