Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001959
(load all 6 compositions to match this statistic)
Mapping
St001959: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => 1
[1,1,0,0]
 => 2
[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]
 => 4
[1,1,1,0,0,0]
 => 3
[1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => 2
[1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => 4
[1,0,1,1,1,0,0,0]
 => 3
[1,1,0,0,1,0,1,0]
 => 2
[1,1,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => 8
[1,1,0,1,1,0,0,0]
 => 6
[1,1,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,0,0]
 => 6
[1,1,1,0,1,0,0,0]
 => 9
[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]
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => 2
[1,0,1,0,1,1,0,1,0,0]
 => 4
[1,0,1,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,0,0,1,0,1,0]
 => 2
[1,0,1,1,0,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,0,1,0,1,0,0]
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => 6
[1,0,1,1,1,0,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => 6
[1,0,1,1,1,0,1,0,0,0]
 => 9
[1,0,1,1,1,1,0,0,0,0]
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => 4
[1,1,0,0,1,1,0,0,1,0]
 => 4
[1,1,0,0,1,1,0,1,0,0]
 => 8
[1,1,0,0,1,1,1,0,0,0]
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => 8
[1,1,0,1,0,1,0,1,0,0]
 => 16
[1,1,0,1,0,1,1,0,0,0]
 => 12
[1,1,0,1,1,0,0,0,1,0]
 => 6
[1,1,0,1,1,0,0,1,0,0]
 => 12
[1,1,0,1,1,0,1,0,0,0]
 => 18
[1,1,0,1,1,1,0,0,0,0]
 => 8
[1,1,1,0,0,0,1,0,1,0]
 => 3
Description
The product of the heights of the peaks of a Dyck path.
Matching statistic: St001813
Mapping
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1,2] => [2,1] => ([],2)
 => 1
[1,1,0,0]
 => [2,1] => [1,2] => ([(0,1)],2)
 => 2
[1,0,1,0,1,0]
 => [1,2,3] => [3,2,1] => ([],3)
 => 1
[1,0,1,1,0,0]
 => [1,3,2] => [3,1,2] => ([(1,2)],3)
 => 2
[1,1,0,0,1,0]
 => [2,1,3] => [2,3,1] => ([(1,2)],3)
 => 2
[1,1,0,1,0,0]
 => [2,3,1] => [2,1,3] => ([(0,2),(1,2)],3)
 => 4
[1,1,1,0,0,0]
 => [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => 3
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [4,3,2,1] => ([],4)
 => 1
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [4,3,1,2] => ([(2,3)],4)
 => 2
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
 => 2
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [4,2,1,3] => ([(1,3),(2,3)],4)
 => 4
[1,0,1,1,1,0,0,0]
 => [1,4,2,3] => [4,1,3,2] => ([(1,2),(1,3)],4)
 => 3
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [3,4,2,1] => ([(2,3)],4)
 => 2
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => 4
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => 4
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => 8
[1,1,0,1,1,0,0,0]
 => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
 => 6
[1,1,1,0,0,0,1,0]
 => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => 3
[1,1,1,0,0,1,0,0]
 => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => 6
[1,1,1,0,1,0,0,0]
 => [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 9
[1,1,1,1,0,0,0,0]
 => [4,1,2,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [5,4,3,2,1] => ([],5)
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [5,4,3,1,2] => ([(3,4)],5)
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [5,4,2,3,1] => ([(3,4)],5)
 => 2
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => 4
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,3,4] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
 => 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [5,3,4,2,1] => ([(3,4)],5)
 => 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => 4
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => 4
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => [5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
 => 6
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,2,3,5] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,2,5,3] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
 => 6
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,2,3] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 9
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,2,3,4] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [4,5,3,2,1] => ([(3,4)],5)
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
 => 4
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => 4
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => 8
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,3,4] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => 8
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 16
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,1,4] => [4,3,1,5,2] => ([(0,4),(1,4),(2,3),(2,4)],5)
 => 12
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,1,3,5] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
 => 6
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 12
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,1,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 18
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,1,3,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
 => 8
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,2,4,5] => [3,5,4,2,1] => ([(2,3),(2,4)],5)
 => 3
Description
The product of the sizes of the principal order filters in a poset.