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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001808
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ 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]
=> [1,1,0,0]
=> 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,0,0]
=> [1,1,1,0,0,0]
=> 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 6
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 3
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 24
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 18
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 16
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 12
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 8
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 12
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 9
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 8
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 6
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 4
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 4
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 120
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> 96
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> 90
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> 72
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> 54
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> 80
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> 64
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> 60
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> 48
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> 36
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> 24
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 16
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 60
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> 48
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> 45
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> 36
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 27
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 40
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> 32
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> 30
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 18
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 8
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
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St001813: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> ([],1)
=> 1
[1,0,1,0]
=> ([(0,1)],2)
=> 2
[1,1,0,0]
=> ([],2)
=> 1
[1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 6
[1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> 4
[1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> 3
[1,1,0,1,0,0]
=> ([(1,2)],3)
=> 2
[1,1,1,0,0,0]
=> ([],3)
=> 1
[1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 24
[1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> 18
[1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 16
[1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> 12
[1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> 8
[1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> 12
[1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 9
[1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> 8
[1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3)],4)
=> 6
[1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> 4
[1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> 4
[1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> 3
[1,1,1,0,1,0,0,0]
=> ([(2,3)],4)
=> 2
[1,1,1,1,0,0,0,0]
=> ([],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 120
[1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 96
[1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 90
[1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 72
[1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> 54
[1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 80
[1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 64
[1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 60
[1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 48
[1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 36
[1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 24
[1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 16
[1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> 60
[1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> 48
[1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 45
[1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> 36
[1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 27
[1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 40
[1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 32
[1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 30
[1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 18
[1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> 8
Description
The product of the sizes of the principal order filters in a poset.
Matching statistic: St000708
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 34% ●values known / values provided: 41%●distinct values known / distinct values provided: 34%
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 34% ●values known / values provided: 41%●distinct values known / distinct values provided: 34%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1]
=> ? = 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1]
=> 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [2,1]
=> 2
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [3,1,1]
=> 3
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 2
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1]
=> 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 4
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 6
[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]
=> [3,3,1,1]
=> 9
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> 4
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> 12
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> 8
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 6
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> 3
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> 4
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> 16
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 12
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 2
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> 8
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 18
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 24
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> 20
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> 36
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> 16
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,2,2,1,1]
=> 8
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> 27
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1,1]
=> 12
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> 32
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 18
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> 30
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> 24
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> 15
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [5,1,1,1,1]
=> 5
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,1,1]
=> 12
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [4,1,1,1,1]
=> 4
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,1,1,1,1]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> 9
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [3,1,1,1,1]
=> 3
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> 16
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 36
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> 48
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,2,1,1,1]
=> 4
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,1,1]
=> 8
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> 32
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> 16
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,1,1]
=> 10
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> 40
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,1,1]
=> 6
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> ? ∊ {40,45,48,60,60,64,72,80,90,96,120}
[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]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [5,5,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [4,4,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [6,5,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [6,2,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [5,4,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [5,2,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [5,3,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [3,3,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [6,3,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [4,3,3,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [4,3,2,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [4,4,4,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
[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]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,1]
=> ? ∊ {18,20,24,24,25,30,30,32,36,36,40,40,45,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720}
Description
The product of the parts of an integer partition.
Matching statistic: St001232
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 11%●distinct values known / distinct values provided: 9%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 11%●distinct values known / distinct values provided: 9%
Values
[1,0]
=> [1] => [1,0]
=> [1,0]
=> 0 = 1 - 1
[1,0,1,0]
=> [2,1] => [1,1,0,0]
=> [1,0,1,0]
=> 1 = 2 - 1
[1,1,0,0]
=> [1,2] => [1,0,1,0]
=> [1,1,0,0]
=> 0 = 1 - 1
[1,0,1,0,1,0]
=> [3,2,1] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? ∊ {4,6} - 1
[1,0,1,1,0,0]
=> [2,3,1] => [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? ∊ {4,6} - 1
[1,1,0,1,0,0]
=> [2,1,3] => [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,12,12,16,18,24} - 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {4,6,8,8,9,10,12,12,15,16,16,16,18,20,20,24,24,27,30,32,32,36,36,40,40,45,48,48,54,60,60,64,72,80,90,96,120} - 1
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4 = 5 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,6,8,8,9,10,12,12,12,15,16,16,16,18,18,20,20,24,24,24,24,25,27,30,30,32,32,32,36,36,36,40,40,45,48,48,48,48,48,50,54,54,60,60,60,64,64,64,72,72,72,72,75,80,80,80,81,90,90,96,96,96,96,96,100,100,108,108,108,120,120,120,120,128,128,135,144,144,144,144,150,160,160,162,162,180,180,180,192,192,192,192,200,200,216,216,216,225,240,240,240,240,256,270,270,288,288,288,300,300,320,324,360,360,360,384,384,400,432,450,480,480,540,576,600,720} - 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 3 - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 5 - 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5 = 6 - 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0 = 1 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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