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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001808
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Mp00028: Dyck paths —reverse⟶ Dyck paths
St001808: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St001808: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1,0,1,0]
=> 2
[1,1,0,0]
=> [1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> 6
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 3
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> 4
[1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> 1
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> 24
[1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> 12
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 16
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 8
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> 4
[1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> 18
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 9
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> 12
[1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0]
=> 6
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 3
[1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> 8
[1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 120
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 60
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 80
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> 40
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 20
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 90
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 45
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> 60
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> 30
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> 15
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 20
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 10
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 5
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 96
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 48
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 64
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 32
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 16
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> 72
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 36
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> 48
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 12
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 32
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 8
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 4
[1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 54
Description
The box weight or horizontal decoration of a Dyck path.
Let a Dyck path $D = (d_1,d_2,\dots,d_n)$ with steps $d_i \in \{N=(0,1),E=(1,0)\}$ be given.
For the $i$th step $d_i \in D$ we define the weight
$$
\beta(d_i) = 1, \quad \text{ if } d_i=N,
$$
and
$$
\beta(d_i) = \sum_{k = 1}^{i} [\![ d_k = N]\!], \quad \text{ if } d_i=E,
$$
where we use the Iverson bracket $[\![ A ]\!]$ that is equal to $1$ if $A$ is true, and $0$ otherwise.
The '''box weight''' or '''horizontal deocration''' of $D$ is defined as
$$
\prod_{i=1}^{n} \beta(d_i).
$$
The name describes the fact that between each $E$ step and the line $y=-1$ exactly one unit box is marked.
Matching statistic: St001813
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(load all 4 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 45%
Mp00065: Permutations —permutation poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 45%
Values
[1,0,1,0]
=> [1,2] => ([(0,1)],2)
=> 2
[1,1,0,0]
=> [2,1] => ([],2)
=> 1
[1,0,1,0,1,0]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 6
[1,0,1,1,0,0]
=> [1,3,2] => ([(0,1),(0,2)],3)
=> 3
[1,1,0,0,1,0]
=> [2,1,3] => ([(0,2),(1,2)],3)
=> 4
[1,1,0,1,0,0]
=> [2,3,1] => ([(1,2)],3)
=> 2
[1,1,1,0,0,0]
=> [3,2,1] => ([],3)
=> 1
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 24
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 12
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 16
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 8
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 4
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 18
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 9
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 12
[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]
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> 3
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 8
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 4
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => ([(2,3)],4)
=> 2
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 120
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> 60
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 80
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> 40
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> 20
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 90
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 45
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 60
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 30
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 15
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 20
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> 10
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> 5
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> 96
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> 48
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 64
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 32
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 16
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 72
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> 36
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 48
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> 12
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 32
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
=> 8
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> 4
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> 54
[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)
=> ? = 5040
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,7,6] => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
=> ? = 2520
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 3360
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,4,6,7,5] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
=> ? = 1680
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,4,7,6,5] => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
=> ? = 840
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,2,3,5,4,7,6] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> ? = 1890
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> ? = 2520
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,4] => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
=> ? = 1260
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,2,3,5,7,6,4] => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
=> ? = 630
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,3,7,5,6,4] => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
=> ? = 420
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 4032
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,4,3,5,7,6] => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> ? = 2016
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,4,3,6,5,7] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> ? = 2688
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,4,3,6,7,5] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
=> ? = 1344
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,4,3,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
=> ? = 672
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 3024
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,4,5,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
=> ? = 1512
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> ? = 2016
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,4,5,6,7,3] => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
=> ? = 1008
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
=> ? = 504
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,4,6,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
=> ? = 1344
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,4,6,5,7,3] => ([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
=> ? = 672
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,4,7,5,6,3] => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)
=> ? = 336
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,4,7,6,5,3] => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
=> ? = 168
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,2,5,4,3,6,7] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ? = 2268
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
=> ? = 1512
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,2,5,4,6,7,3] => ([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ? = 756
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,2,6,4,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
=> ? = 1008
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,2,6,4,5,7,3] => ([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
=> ? = 504
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,2,7,4,5,6,3] => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
=> ? = 252
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,2,7,4,6,5,3] => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
=> ? = 126
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,2,7,5,6,4,3] => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
=> ? = 84
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 4200
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,3,2,4,5,7,6] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> ? = 2100
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,3,2,4,6,7,5] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
=> ? = 1400
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,3,2,5,6,4,7] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> ? = 2100
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,3,2,5,6,7,4] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> ? = 1050
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> ? = 3360
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,3,4,2,6,5,7] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
=> ? = 2240
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,3,4,2,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> ? = 1120
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,3,4,2,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
=> ? = 560
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ? = 2520
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,3,4,5,2,7,6] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> ? = 1260
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ? = 1680
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,7,2] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 840
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,3,4,5,7,6,2] => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> ? = 420
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
=> ? = 1120
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,3,4,6,5,7,2] => ([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)
=> ? = 560
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,3,4,7,5,6,2] => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
=> ? = 280
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,4,7,6,5,2] => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
=> ? = 140
Description
The product of the sizes of the principal order filters in a poset.
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