Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001929
(load all 20 compositions to match this statistic)
Mapping
St001929: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 1
[1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => 2
[1,1,0,1,0,0]
 => 1
[1,1,1,0,0,0]
 => 2
[1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => 3
[1,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,0,1,0,0]
 => 3
[1,0,1,1,1,0,0,0]
 => 4
[1,1,0,0,1,0,1,0]
 => 3
[1,1,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,0,1,0]
 => 3
[1,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,0,0,1,0]
 => 4
[1,1,1,0,0,1,0,0]
 => 3
[1,1,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0]
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => 4
[1,0,1,0,1,1,0,0,1,0]
 => 4
[1,0,1,0,1,1,0,1,0,0]
 => 6
[1,0,1,0,1,1,1,0,0,0]
 => 6
[1,0,1,1,0,0,1,0,1,0]
 => 4
[1,0,1,1,0,0,1,1,0,0]
 => 8
[1,0,1,1,0,1,0,0,1,0]
 => 6
[1,0,1,1,0,1,0,1,0,0]
 => 4
[1,0,1,1,0,1,1,0,0,0]
 => 8
[1,0,1,1,1,0,0,0,1,0]
 => 6
[1,0,1,1,1,0,0,1,0,0]
 => 8
[1,0,1,1,1,0,1,0,0,0]
 => 6
[1,0,1,1,1,1,0,0,0,0]
 => 10
[1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,0,1,0,1,1,0,0]
 => 8
[1,1,0,0,1,1,0,0,1,0]
 => 8
[1,1,0,0,1,1,0,1,0,0]
 => 6
[1,1,0,0,1,1,1,0,0,0]
 => 10
[1,1,0,1,0,0,1,0,1,0]
 => 6
[1,1,0,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => 4
[1,1,0,1,1,0,0,0,1,0]
 => 8
[1,1,0,1,1,0,0,1,0,0]
 => 4
[1,1,0,1,1,0,1,0,0,0]
 => 6
[1,1,0,1,1,1,0,0,0,0]
 => 6
Description
The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path.
Matching statistic: St001633
Mapping
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001633: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 4%
Values
[1,0]
 => [1,0]
 => [1] => ([],1)
 => 0 = 1 - 1
[1,0,1,0]
 => [1,1,0,0]
 => [2,1] => ([(0,1)],2)
 => 0 = 1 - 1
[1,1,0,0]
 => [1,0,1,0]
 => [1,2] => ([(0,1)],2)
 => 0 = 1 - 1
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [3,2,1] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => 2 = 3 - 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 4 - 1
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 4 - 1
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 3 - 1
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 4 - 1
[1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 3 - 1
[1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 4 - 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 4 - 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => ([(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)
 => ? = 6 - 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 4 - 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 8 - 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 6 - 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 8 - 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 6 - 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 8 - 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 6 - 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
 => ? = 10 - 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 8 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 8 - 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 10 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => ([(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)
 => ? = 6 - 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 4 - 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 8 - 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
 => ? = 4 - 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 6 - 1
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 10 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 8 - 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 4 - 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 8 - 1
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 6 - 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 6 - 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 8 - 1
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
 => ? = 10 - 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 6 - 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 8 - 1
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 6 - 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 10 - 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]
 => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => ([(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)
 => ? = 5 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 5 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,3,2,1,5,6] => ([(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)
 => ? = 10 - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,4,3,2,6,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 8 - 1
[1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[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]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.