Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000725
(load all 4 compositions to match this statistic)
Mapping
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000725: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [[1],[2]]
 => [2,1] => 2
[1,0,1,0]
 => [[1,3],[2,4]]
 => [2,4,1,3] => 3
[1,1,0,0]
 => [[1,2],[3,4]]
 => [3,4,1,2] => 2
[1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => [2,4,6,1,3,5] => 5
[1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => [2,5,6,1,3,4] => 4
[1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => [3,4,6,1,2,5] => 5
[1,1,0,1,0,0]
 => [[1,2,4],[3,5,6]]
 => [3,5,6,1,2,4] => 4
[1,1,1,0,0,0]
 => [[1,2,3],[4,5,6]]
 => [4,5,6,1,2,3] => 3
[1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => [2,4,6,8,1,3,5,7] => 7
[1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => [2,4,7,8,1,3,5,6] => 6
[1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => [2,5,6,8,1,3,4,7] => 7
[1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => [2,5,7,8,1,3,4,6] => 6
[1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => [2,6,7,8,1,3,4,5] => 5
[1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => [3,4,6,8,1,2,5,7] => 7
[1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => [3,4,7,8,1,2,5,6] => 6
[1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => [3,5,6,8,1,2,4,7] => 7
[1,1,0,1,0,1,0,0]
 => [[1,2,4,6],[3,5,7,8]]
 => [3,5,7,8,1,2,4,6] => 6
[1,1,0,1,1,0,0,0]
 => [[1,2,4,5],[3,6,7,8]]
 => [3,6,7,8,1,2,4,5] => 5
[1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => [4,5,6,8,1,2,3,7] => 7
[1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => [4,5,7,8,1,2,3,6] => 6
[1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => [4,6,7,8,1,2,3,5] => 5
[1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => [5,6,7,8,1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => [2,4,6,8,10,1,3,5,7,9] => 9
[1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,8],[2,4,6,9,10]]
 => [2,4,6,9,10,1,3,5,7,8] => 8
[1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,6,9],[2,4,7,8,10]]
 => [2,4,7,8,10,1,3,5,6,9] => 9
[1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,6,8],[2,4,7,9,10]]
 => [2,4,7,9,10,1,3,5,6,8] => 8
[1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,6,7],[2,4,8,9,10]]
 => [2,4,8,9,10,1,3,5,6,7] => 7
[1,0,1,1,0,0,1,0,1,0]
 => [[1,3,4,7,9],[2,5,6,8,10]]
 => [2,5,6,8,10,1,3,4,7,9] => 9
[1,0,1,1,0,0,1,1,0,0]
 => [[1,3,4,7,8],[2,5,6,9,10]]
 => [2,5,6,9,10,1,3,4,7,8] => 8
[1,0,1,1,0,1,0,0,1,0]
 => [[1,3,4,6,9],[2,5,7,8,10]]
 => [2,5,7,8,10,1,3,4,6,9] => 9
[1,0,1,1,0,1,0,1,0,0]
 => [[1,3,4,6,8],[2,5,7,9,10]]
 => [2,5,7,9,10,1,3,4,6,8] => 8
[1,0,1,1,0,1,1,0,0,0]
 => [[1,3,4,6,7],[2,5,8,9,10]]
 => [2,5,8,9,10,1,3,4,6,7] => 7
[1,0,1,1,1,0,0,0,1,0]
 => [[1,3,4,5,9],[2,6,7,8,10]]
 => [2,6,7,8,10,1,3,4,5,9] => 9
[1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => [2,6,7,9,10,1,3,4,5,8] => 8
[1,0,1,1,1,0,1,0,0,0]
 => [[1,3,4,5,7],[2,6,8,9,10]]
 => [2,6,8,9,10,1,3,4,5,7] => 7
[1,0,1,1,1,1,0,0,0,0]
 => [[1,3,4,5,6],[2,7,8,9,10]]
 => [2,7,8,9,10,1,3,4,5,6] => 6
[1,1,0,0,1,0,1,0,1,0]
 => [[1,2,5,7,9],[3,4,6,8,10]]
 => [3,4,6,8,10,1,2,5,7,9] => 9
[1,1,0,0,1,0,1,1,0,0]
 => [[1,2,5,7,8],[3,4,6,9,10]]
 => [3,4,6,9,10,1,2,5,7,8] => 8
[1,1,0,0,1,1,0,0,1,0]
 => [[1,2,5,6,9],[3,4,7,8,10]]
 => [3,4,7,8,10,1,2,5,6,9] => 9
[1,1,0,0,1,1,0,1,0,0]
 => [[1,2,5,6,8],[3,4,7,9,10]]
 => [3,4,7,9,10,1,2,5,6,8] => 8
[1,1,0,0,1,1,1,0,0,0]
 => [[1,2,5,6,7],[3,4,8,9,10]]
 => [3,4,8,9,10,1,2,5,6,7] => 7
[1,1,0,1,0,0,1,0,1,0]
 => [[1,2,4,7,9],[3,5,6,8,10]]
 => [3,5,6,8,10,1,2,4,7,9] => 9
[1,1,0,1,0,0,1,1,0,0]
 => [[1,2,4,7,8],[3,5,6,9,10]]
 => [3,5,6,9,10,1,2,4,7,8] => 8
[1,1,0,1,0,1,0,0,1,0]
 => [[1,2,4,6,9],[3,5,7,8,10]]
 => [3,5,7,8,10,1,2,4,6,9] => 9
[1,1,0,1,0,1,0,1,0,0]
 => [[1,2,4,6,8],[3,5,7,9,10]]
 => [3,5,7,9,10,1,2,4,6,8] => 8
[1,1,0,1,0,1,1,0,0,0]
 => [[1,2,4,6,7],[3,5,8,9,10]]
 => [3,5,8,9,10,1,2,4,6,7] => 7
[1,1,0,1,1,0,0,0,1,0]
 => [[1,2,4,5,9],[3,6,7,8,10]]
 => [3,6,7,8,10,1,2,4,5,9] => 9
[1,1,0,1,1,0,0,1,0,0]
 => [[1,2,4,5,8],[3,6,7,9,10]]
 => [3,6,7,9,10,1,2,4,5,8] => 8
[1,1,0,1,1,0,1,0,0,0]
 => [[1,2,4,5,7],[3,6,8,9,10]]
 => [3,6,8,9,10,1,2,4,5,7] => 7
[1,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,5,6],[3,7,8,9,10]]
 => [3,7,8,9,10,1,2,4,5,6] => 6
Description
The smallest label of a leaf of the increasing binary tree associated to a permutation.
Matching statistic: St000438
(load all 92 compositions to match this statistic)
Mapping
St000438: Dyck paths ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => ? = 2
[1,0,1,0]
 => 3
[1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => 5
[1,0,1,1,0,0]
 => 4
[1,1,0,0,1,0]
 => 5
[1,1,0,1,0,0]
 => 4
[1,1,1,0,0,0]
 => 3
[1,0,1,0,1,0,1,0]
 => 7
[1,0,1,0,1,1,0,0]
 => 6
[1,0,1,1,0,0,1,0]
 => 7
[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]
 => 7
[1,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,0,1,0]
 => 7
[1,1,0,1,0,1,0,0]
 => 6
[1,1,0,1,1,0,0,0]
 => 5
[1,1,1,0,0,0,1,0]
 => 7
[1,1,1,0,0,1,0,0]
 => 6
[1,1,1,0,1,0,0,0]
 => 5
[1,1,1,1,0,0,0,0]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => 9
[1,0,1,0,1,0,1,1,0,0]
 => 8
[1,0,1,0,1,1,0,0,1,0]
 => 9
[1,0,1,0,1,1,0,1,0,0]
 => 8
[1,0,1,0,1,1,1,0,0,0]
 => 7
[1,0,1,1,0,0,1,0,1,0]
 => 9
[1,0,1,1,0,0,1,1,0,0]
 => 8
[1,0,1,1,0,1,0,0,1,0]
 => 9
[1,0,1,1,0,1,0,1,0,0]
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => 7
[1,0,1,1,1,0,0,0,1,0]
 => 9
[1,0,1,1,1,0,0,1,0,0]
 => 8
[1,0,1,1,1,0,1,0,0,0]
 => 7
[1,0,1,1,1,1,0,0,0,0]
 => 6
[1,1,0,0,1,0,1,0,1,0]
 => 9
[1,1,0,0,1,0,1,1,0,0]
 => 8
[1,1,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,0,1,1,0,1,0,0]
 => 8
[1,1,0,0,1,1,1,0,0,0]
 => 7
[1,1,0,1,0,0,1,0,1,0]
 => 9
[1,1,0,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => 9
[1,1,0,1,0,1,0,1,0,0]
 => 8
[1,1,0,1,0,1,1,0,0,0]
 => 7
[1,1,0,1,1,0,0,0,1,0]
 => 9
[1,1,0,1,1,0,0,1,0,0]
 => 8
[1,1,0,1,1,0,1,0,0,0]
 => 7
[1,1,0,1,1,1,0,0,0,0]
 => 6
[1,1,1,0,0,0,1,0,1,0]
 => 9
Description
The position of the last up step in a Dyck path.
Matching statistic: St000641
(load all 3 compositions to match this statistic)
Mapping
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000641: Posets ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [.,.]
 => [1] => ([],1)
 => ? = 2
[1,0,1,0]
 => [[.,.],.]
 => [1,2] => ([(0,1)],2)
 => 3
[1,1,0,0]
 => [.,[.,.]]
 => [2,1] => ([],2)
 => 2
[1,0,1,0,1,0]
 => [[[.,.],.],.]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 5
[1,0,1,1,0,0]
 => [[.,.],[.,.]]
 => [3,1,2] => ([(1,2)],3)
 => 4
[1,1,0,0,1,0]
 => [[.,[.,.]],.]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => 5
[1,1,0,1,0,0]
 => [.,[[.,.],.]]
 => [2,3,1] => ([(1,2)],3)
 => 4
[1,1,1,0,0,0]
 => [.,[.,[.,.]]]
 => [3,2,1] => ([],3)
 => 3
[1,0,1,0,1,0,1,0]
 => [[[[.,.],.],.],.]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 7
[1,0,1,0,1,1,0,0]
 => [[[.,.],.],[.,.]]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => 6
[1,0,1,1,0,0,1,0]
 => [[[.,.],[.,.]],.]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => 7
[1,0,1,1,0,1,0,0]
 => [[.,.],[[.,.],.]]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => 6
[1,0,1,1,1,0,0,0]
 => [[.,.],[.,[.,.]]]
 => [4,3,1,2] => ([(2,3)],4)
 => 5
[1,1,0,0,1,0,1,0]
 => [[[.,[.,.]],.],.]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => 7
[1,1,0,0,1,1,0,0]
 => [[.,[.,.]],[.,.]]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => 6
[1,1,0,1,0,0,1,0]
 => [[.,[[.,.],.]],.]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => 7
[1,1,0,1,0,1,0,0]
 => [.,[[[.,.],.],.]]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => 6
[1,1,0,1,1,0,0,0]
 => [.,[[.,.],[.,.]]]
 => [4,2,3,1] => ([(2,3)],4)
 => 5
[1,1,1,0,0,0,1,0]
 => [[.,[.,[.,.]]],.]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => 7
[1,1,1,0,0,1,0,0]
 => [.,[[.,[.,.]],.]]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => 6
[1,1,1,0,1,0,0,0]
 => [.,[.,[[.,.],.]]]
 => [3,4,2,1] => ([(2,3)],4)
 => 5
[1,1,1,1,0,0,0,0]
 => [.,[.,[.,[.,.]]]]
 => [4,3,2,1] => ([],4)
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [[[[[.,.],.],.],.],.]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 9
[1,0,1,0,1,0,1,1,0,0]
 => [[[[.,.],.],.],[.,.]]
 => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => 8
[1,0,1,0,1,1,0,0,1,0]
 => [[[[.,.],.],[.,.]],.]
 => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 9
[1,0,1,0,1,1,0,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => 8
[1,0,1,0,1,1,1,0,0,0]
 => [[[.,.],.],[.,[.,.]]]
 => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => 7
[1,0,1,1,0,0,1,0,1,0]
 => [[[[.,.],[.,.]],.],.]
 => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 9
[1,0,1,1,0,0,1,1,0,0]
 => [[[.,.],[.,.]],[.,.]]
 => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
 => 8
[1,0,1,1,0,1,0,0,1,0]
 => [[[.,.],[[.,.],.]],.]
 => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 9
[1,0,1,1,0,1,0,1,0,0]
 => [[.,.],[[[.,.],.],.]]
 => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => 7
[1,0,1,1,1,0,0,0,1,0]
 => [[[.,.],[.,[.,.]]],.]
 => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 9
[1,0,1,1,1,0,0,1,0,0]
 => [[.,.],[[.,[.,.]],.]]
 => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
 => 8
[1,0,1,1,1,0,1,0,0,0]
 => [[.,.],[.,[[.,.],.]]]
 => [4,5,3,1,2] => ([(1,4),(2,3)],5)
 => 7
[1,0,1,1,1,1,0,0,0,0]
 => [[.,.],[.,[.,[.,.]]]]
 => [5,4,3,1,2] => ([(3,4)],5)
 => 6
[1,1,0,0,1,0,1,0,1,0]
 => [[[[.,[.,.]],.],.],.]
 => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 9
[1,1,0,0,1,0,1,1,0,0]
 => [[[.,[.,.]],.],[.,.]]
 => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
 => 8
[1,1,0,0,1,1,0,0,1,0]
 => [[[.,[.,.]],[.,.]],.]
 => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 9
[1,1,0,0,1,1,0,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => 8
[1,1,0,0,1,1,1,0,0,0]
 => [[.,[.,.]],[.,[.,.]]]
 => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => 7
[1,1,0,1,0,0,1,0,1,0]
 => [[[.,[[.,.],.]],.],.]
 => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 9
[1,1,0,1,0,0,1,1,0,0]
 => [[.,[[.,.],.]],[.,.]]
 => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => [[.,[[[.,.],.],.]],.]
 => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 9
[1,1,0,1,0,1,0,1,0,0]
 => [.,[[[[.,.],.],.],.]]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => 8
[1,1,0,1,0,1,1,0,0,0]
 => [.,[[[.,.],.],[.,.]]]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => 7
[1,1,0,1,1,0,0,0,1,0]
 => [[.,[[.,.],[.,.]]],.]
 => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 9
[1,1,0,1,1,0,0,1,0,0]
 => [.,[[[.,.],[.,.]],.]]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => 8
[1,1,0,1,1,0,1,0,0,0]
 => [.,[[.,.],[[.,.],.]]]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => 7
[1,1,0,1,1,1,0,0,0,0]
 => [.,[[.,.],[.,[.,.]]]]
 => [5,4,2,3,1] => ([(3,4)],5)
 => 6
[1,1,1,0,0,0,1,0,1,0]
 => [[[.,[.,[.,.]]],.],.]
 => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 9
Description
The number of non-empty boolean intervals in a poset.
Matching statistic: St000874
Mapping
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St000874: Dyck paths ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1,0]
 => [1,0]
 => [1,0]
 => ? = 2 - 2
[1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => [1,1,0,0]
 => 1 = 3 - 2
[1,1,0,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => 0 = 2 - 2
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 3 = 5 - 2
[1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 2 = 4 - 2
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 3 = 5 - 2
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 2 = 4 - 2
[1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1 = 3 - 2
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 5 = 7 - 2
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 4 = 6 - 2
[1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 5 = 7 - 2
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 4 = 6 - 2
[1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 3 = 5 - 2
[1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => 5 = 7 - 2
[1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 4 = 6 - 2
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 5 = 7 - 2
[1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 4 = 6 - 2
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 3 = 5 - 2
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 5 = 7 - 2
[1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 4 = 6 - 2
[1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 3 = 5 - 2
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 2 = 4 - 2
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 4 = 6 - 2
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 7 = 9 - 2
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 6 = 8 - 2
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 7 - 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 4 = 6 - 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 7 = 9 - 2
Description
The position of the last double rise in a Dyck path. If the Dyck path has no double rises, this statistic is $0$.
Matching statistic: St001880
(load all 2 compositions to match this statistic)
Mapping
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
[1,0]
 => [1,0]
 => [1,1,0,0]
 => ([(0,1)],2)
 => ? = 2 + 1
[1,0,1,0]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[1,1,0,0]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6 = 5 + 1
[1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5 = 4 + 1
[1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 6 = 5 + 1
[1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5 = 4 + 1
[1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 7 + 1
[1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => 7 = 6 + 1
[1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 7 + 1
[1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => 7 = 6 + 1
[1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6 = 5 + 1
[1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 7 + 1
[1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => 7 = 6 + 1
[1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 7 + 1
[1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => 7 = 6 + 1
[1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 6 = 5 + 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 7 + 1
[1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => 7 = 6 + 1
[1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 6 = 5 + 1
[1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => ? = 9 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 8 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => ? = 9 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ? = 8 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ? = 9 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ? = 8 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 9 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ? = 8 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ? = 7 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
 => ? = 9 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ? = 8 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 7 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => 7 = 6 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 8 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ? = 9 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 8 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 7 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ? = 9 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ? = 8 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 9 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ? = 8 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 7 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ? = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ? = 8 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ? = 7 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => 7 = 6 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ? = 9 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ? = 8 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ? = 9 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ? = 8 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 7 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ? = 9 + 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ? = 8 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 7 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => 7 = 6 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
 => ? = 9 + 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 8 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 7 + 1
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => 7 = 6 + 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 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]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
 => ? = 11 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
 => ? = 10 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
 => ? = 11 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
 => ? = 10 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ([(0,5),(1,9),(2,8),(3,2),(3,7),(4,1),(4,7),(5,6),(6,3),(6,4),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 9 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => ([(0,5),(0,6),(1,10),(2,11),(3,4),(3,14),(4,8),(5,2),(5,13),(6,3),(6,13),(8,9),(9,7),(10,7),(11,1),(11,12),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
 => ? = 11 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12)
 => ? = 10 + 1
[1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001406
Mapping
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St001406: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 60%
Values
[1,0]
 => [1] => [[1]]
 => [[1]]
 => ? = 2
[1,0,1,0]
 => [2,1] => [[1],[2]]
 => [[1,1],[1]]
 => 3
[1,1,0,0]
 => [1,2] => [[1,2]]
 => [[2,0],[1]]
 => 2
[1,0,1,0,1,0]
 => [2,1,3] => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 5
[1,0,1,1,0,0]
 => [2,3,1] => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 4
[1,1,0,0,1,0]
 => [3,1,2] => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 5
[1,1,0,1,0,0]
 => [1,3,2] => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 4
[1,1,1,0,0,0]
 => [1,2,3] => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 3
[1,0,1,0,1,0,1,0]
 => [2,1,4,3] => [[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 7
[1,0,1,0,1,1,0,0]
 => [2,4,1,3] => [[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => 6
[1,0,1,1,0,0,1,0]
 => [2,1,3,4] => [[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 7
[1,0,1,1,0,1,0,0]
 => [2,3,1,4] => [[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 6
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 5
[1,1,0,0,1,0,1,0]
 => [3,1,4,2] => [[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 7
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => 6
[1,1,0,1,0,0,1,0]
 => [3,1,2,4] => [[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 7
[1,1,0,1,0,1,0,0]
 => [1,3,2,4] => [[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 6
[1,1,0,1,1,0,0,0]
 => [1,3,4,2] => [[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 5
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 7
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 6
[1,1,1,0,1,0,0,0]
 => [1,2,4,3] => [[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 5
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [2,1,4,3,5] => [[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => [[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,0,1,0,1,1,0,0,1,0]
 => [2,1,4,5,3] => [[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,0,1,0,1,1,0,1,0,0]
 => [2,4,1,5,3] => [[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,0,1,0,1,1,1,0,0,0]
 => [2,4,5,1,3] => [[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,5,3,4] => [[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,0,1,1,0,0,1,1,0,0]
 => [2,5,1,3,4] => [[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,0,1,1,0,1,0,0,1,0]
 => [2,1,3,5,4] => [[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => [[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,0,1,1,0,1,1,0,0,0]
 => [2,3,5,1,4] => [[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,4,5] => [[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,0,1,1,1,0,0,1,0,0]
 => [2,3,1,4,5] => [[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,0,1,1,1,0,1,0,0,0]
 => [2,3,4,1,5] => [[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 6
[1,1,0,0,1,0,1,0,1,0]
 => [3,1,4,2,5] => [[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,0,0,1,0,1,1,0,0]
 => [3,4,1,2,5] => [[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,0,0,1,1,0,0,1,0]
 => [3,1,4,5,2] => [[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,0,0,1,1,0,1,0,0]
 => [3,4,1,5,2] => [[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,5,2,4] => [[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,0,1,0,0,1,1,0,0]
 => [3,5,1,2,4] => [[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,0,1,0,1,0,0,1,0]
 => [3,1,2,5,4] => [[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => [[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => [[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,4,5] => [[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,0,1,1,0,0,1,0,0]
 => [1,3,2,4,5] => [[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,0,1,1,0,1,0,0,0]
 => [1,3,4,2,5] => [[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,0,1,1,1,0,0,0,0]
 => [1,3,4,5,2] => [[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 6
[1,1,1,0,0,0,1,0,1,0]
 => [4,1,5,2,3] => [[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,1,0,0,1,0,0,1,0]
 => [4,1,2,5,3] => [[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,1,0,0,1,0,1,0,0]
 => [1,4,2,5,3] => [[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,1,0,0,1,1,0,0,0]
 => [1,4,5,2,3] => [[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,3,5] => [[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,1,0,1,0,0,1,0,0]
 => [1,4,2,3,5] => [[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,1,0,1,0,1,0,0,0]
 => [1,2,4,3,5] => [[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,1,0,1,1,0,0,0,0]
 => [1,2,4,5,3] => [[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 6
[1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => [[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 9
[1,1,1,1,0,0,0,1,0,0]
 => [1,5,2,3,4] => [[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 8
[1,1,1,1,0,0,1,0,0,0]
 => [1,2,5,3,4] => [[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 7
[1,1,1,1,0,1,0,0,0,0]
 => [1,2,3,5,4] => [[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 6
[1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => [[1,2,3,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
 => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 11
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,6,5] => [[1,2,5],[3,4,6]]
 => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 10
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [2,1,4,6,3,5] => [[1,3,4],[2,5,6]]
 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 11
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [2,4,1,6,3,5] => [[1,2,4],[3,5,6]]
 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 10
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [2,4,6,1,3,5] => [[1,2,3],[4,5,6]]
 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 9
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 11
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [2,4,1,3,5,6] => [[1,2,5,6],[3,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 10
Description
The number of nonzero entries in a Gelfand Tsetlin pattern.