Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000059
(load all 3 compositions to match this statistic)
Mapping
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000059: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [[1],[2]]
 => 1
[1,0,1,0]
 => [[1,3],[2,4]]
 => 2
[1,1,0,0]
 => [[1,2],[3,4]]
 => 4
[1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 3
[1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 5
[1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 5
[1,1,0,1,0,0]
 => [[1,2,4],[3,5,6]]
 => 8
[1,1,1,0,0,0]
 => [[1,2,3],[4,5,6]]
 => 9
[1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => 4
[1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => 6
[1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => 6
[1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => 9
[1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => 10
[1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => 6
[1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => 8
[1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => 9
[1,1,0,1,0,1,0,0]
 => [[1,2,4,6],[3,5,7,8]]
 => 13
[1,1,0,1,1,0,0,0]
 => [[1,2,4,5],[3,6,7,8]]
 => 14
[1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => 10
[1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 14
[1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 15
[1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 16
[1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => 5
[1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,8],[2,4,6,9,10]]
 => 7
[1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,6,9],[2,4,7,8,10]]
 => 7
[1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,6,8],[2,4,7,9,10]]
 => 10
[1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,6,7],[2,4,8,9,10]]
 => 11
[1,0,1,1,0,0,1,0,1,0]
 => [[1,3,4,7,9],[2,5,6,8,10]]
 => 7
[1,0,1,1,0,0,1,1,0,0]
 => [[1,3,4,7,8],[2,5,6,9,10]]
 => 9
[1,0,1,1,0,1,0,0,1,0]
 => [[1,3,4,6,9],[2,5,7,8,10]]
 => 10
[1,0,1,1,0,1,0,1,0,0]
 => [[1,3,4,6,8],[2,5,7,9,10]]
 => 14
[1,0,1,1,0,1,1,0,0,0]
 => [[1,3,4,6,7],[2,5,8,9,10]]
 => 15
[1,0,1,1,1,0,0,0,1,0]
 => [[1,3,4,5,9],[2,6,7,8,10]]
 => 11
[1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => 15
[1,0,1,1,1,0,1,0,0,0]
 => [[1,3,4,5,7],[2,6,8,9,10]]
 => 16
[1,0,1,1,1,1,0,0,0,0]
 => [[1,3,4,5,6],[2,7,8,9,10]]
 => 17
[1,1,0,0,1,0,1,0,1,0]
 => [[1,2,5,7,9],[3,4,6,8,10]]
 => 7
[1,1,0,0,1,0,1,1,0,0]
 => [[1,2,5,7,8],[3,4,6,9,10]]
 => 9
[1,1,0,0,1,1,0,0,1,0]
 => [[1,2,5,6,9],[3,4,7,8,10]]
 => 9
[1,1,0,0,1,1,0,1,0,0]
 => [[1,2,5,6,8],[3,4,7,9,10]]
 => 12
[1,1,0,0,1,1,1,0,0,0]
 => [[1,2,5,6,7],[3,4,8,9,10]]
 => 13
[1,1,0,1,0,0,1,0,1,0]
 => [[1,2,4,7,9],[3,5,6,8,10]]
 => 10
[1,1,0,1,0,0,1,1,0,0]
 => [[1,2,4,7,8],[3,5,6,9,10]]
 => 12
[1,1,0,1,0,1,0,0,1,0]
 => [[1,2,4,6,9],[3,5,7,8,10]]
 => 14
[1,1,0,1,0,1,0,1,0,0]
 => [[1,2,4,6,8],[3,5,7,9,10]]
 => 19
[1,1,0,1,0,1,1,0,0,0]
 => [[1,2,4,6,7],[3,5,8,9,10]]
 => 20
[1,1,0,1,1,0,0,0,1,0]
 => [[1,2,4,5,9],[3,6,7,8,10]]
 => 15
[1,1,0,1,1,0,0,1,0,0]
 => [[1,2,4,5,8],[3,6,7,9,10]]
 => 20
[1,1,0,1,1,0,1,0,0,0]
 => [[1,2,4,5,7],[3,6,8,9,10]]
 => 21
[1,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,5,6],[3,7,8,9,10]]
 => 22
Description
The inversion number of a standard tableau as defined by Haglund and Stevens. Their inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b), where the inversion path is defined in detail in [1].
Matching statistic: St001879
(load all 2 compositions to match this statistic)
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 33%
Values
[1,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => ([(0,1)],2)
 => ? = 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 2
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => ([(1,2)],3)
 => ? = 4
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {5,5,8,9}
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(3,1)],4)
 => ? ∊ {5,5,8,9}
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {5,5,8,9}
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => ? ∊ {5,5,8,9}
[1,0,1,0,1,0,1,0]
 => [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
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 6
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(2,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(1,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ([(1,4),(2,3),(2,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => ([(3,4)],5)
 => ? ∊ {6,6,8,9,9,10,10,13,14,14,15,16}
[1,0,1,0,1,0,1,0,1,0]
 => [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
[1,0,1,0,1,0,1,1,0,0]
 => [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),(1,3),(3,5),(4,2),(5,4)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 7
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 7
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => 12
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => ([(1,5),(2,5),(3,4),(3,5)],6)
 => ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,14,14,15,15,15,15,16,16,17,17,19,20,20,20,21,21,21,22,22,22,23,23,24,25}
[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]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => 8
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 8
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => 8
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
 => 13
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
 => 8
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => 11
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => 8
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
 => 13
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
 => 13
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
 => 12
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 14
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
 => 20
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.