searching the database
Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001808
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
St001808: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> 2
[1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> 6
[1,0,1,1,0,0]
=> 4
[1,1,0,0,1,0]
=> 3
[1,1,0,1,0,0]
=> 2
[1,1,1,0,0,0]
=> 1
[1,0,1,0,1,0,1,0]
=> 24
[1,0,1,0,1,1,0,0]
=> 18
[1,0,1,1,0,0,1,0]
=> 16
[1,0,1,1,0,1,0,0]
=> 12
[1,0,1,1,1,0,0,0]
=> 8
[1,1,0,0,1,0,1,0]
=> 12
[1,1,0,0,1,1,0,0]
=> 9
[1,1,0,1,0,0,1,0]
=> 8
[1,1,0,1,0,1,0,0]
=> 6
[1,1,0,1,1,0,0,0]
=> 4
[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]
=> 2
[1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> 120
[1,0,1,0,1,0,1,1,0,0]
=> 96
[1,0,1,0,1,1,0,0,1,0]
=> 90
[1,0,1,0,1,1,0,1,0,0]
=> 72
[1,0,1,0,1,1,1,0,0,0]
=> 54
[1,0,1,1,0,0,1,0,1,0]
=> 80
[1,0,1,1,0,0,1,1,0,0]
=> 64
[1,0,1,1,0,1,0,0,1,0]
=> 60
[1,0,1,1,0,1,0,1,0,0]
=> 48
[1,0,1,1,0,1,1,0,0,0]
=> 36
[1,0,1,1,1,0,0,0,1,0]
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> 24
[1,0,1,1,1,1,0,0,0,0]
=> 16
[1,1,0,0,1,0,1,0,1,0]
=> 60
[1,1,0,0,1,0,1,1,0,0]
=> 48
[1,1,0,0,1,1,0,0,1,0]
=> 45
[1,1,0,0,1,1,0,1,0,0]
=> 36
[1,1,0,0,1,1,1,0,0,0]
=> 27
[1,1,0,1,0,0,1,0,1,0]
=> 40
[1,1,0,1,0,0,1,1,0,0]
=> 32
[1,1,0,1,0,1,0,0,1,0]
=> 30
[1,1,0,1,0,1,0,1,0,0]
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> 18
[1,1,0,1,1,0,0,0,1,0]
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> 8
[1,1,1,0,0,0,1,0,1,0]
=> 20
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 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 45%
Mp00069: Permutations —complement⟶ Permutations
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]
=> [2,1] => [1,2] => ([(0,1)],2)
=> 2
[1,1,0,0]
=> [1,2] => [2,1] => ([],2)
=> 1
[1,0,1,0,1,0]
=> [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 6
[1,0,1,1,0,0]
=> [2,3,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> 4
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => ([(0,1),(0,2)],3)
=> 3
[1,1,0,1,0,0]
=> [2,1,3] => [2,3,1] => ([(1,2)],3)
=> 2
[1,1,1,0,0,0]
=> [1,2,3] => [3,2,1] => ([],3)
=> 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 24
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 18
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 16
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 12
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 8
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 12
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 9
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 8
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> 6
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> 4
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 4
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> 3
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [3,4,2,1] => ([(2,3)],4)
=> 2
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4,3,2,1] => ([],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [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]
=> [4,5,3,2,1] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> 96
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 90
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> 72
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
=> 54
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 80
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 64
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [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]
=> [4,3,2,5,1] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> 48
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
=> 36
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [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]
=> [4,2,3,5,1] => [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 24
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 16
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> 60
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [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]
=> [5,3,4,1,2] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 45
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> 36
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 27
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> 40
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 32
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 30
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> 18
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [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]
=> [3,2,4,1,5] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> 8
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> 20
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 5040
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 4200
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 3600
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 4032
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> ? = 3360
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [6,5,4,7,3,2,1] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 2880
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ? = 2688
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,2,1] => [2,4,3,1,5,6,7] => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 2304
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [6,5,7,3,4,2,1] => [2,3,1,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> ? = 2700
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 3024
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ? = 2520
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [6,4,5,3,7,2,1] => [2,4,3,5,1,6,7] => ([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
=> ? = 1728
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 1440
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [7,6,3,4,5,2,1] => [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
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,5,2,1] => [2,1,5,4,3,6,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
=> ? = 1944
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ? = 1890
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,7,2,1] => [2,3,5,4,1,6,7] => ([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
=> ? = 1620
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
=> ? = 1296
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 3360
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [7,6,4,5,2,3,1] => [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
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [7,5,4,6,2,3,1] => [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
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [6,5,4,7,2,3,1] => [2,3,4,1,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> ? = 1920
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,2,3,1] => [2,4,3,1,6,5,7] => ([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
=> ? = 1536
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> ? = 2520
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [7,5,6,3,2,4,1] => [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
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [6,5,7,3,2,4,1] => [2,3,1,5,6,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ? = 1800
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> [7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
=> ? = 2016
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [7,5,4,3,2,6,1] => [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]
=> [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 1440
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ? = 1344
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [7,6,3,4,2,5,1] => [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
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,2,5,1] => [2,1,5,4,6,3,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
=> ? = 1296
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,2,7,1] => [2,3,5,4,6,1,7] => ([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1080
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ? = 1008
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,2,7,1] => [2,4,5,3,6,1,7] => ([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
=> ? = 864
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 720
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [6,3,4,5,2,7,1] => [2,5,4,3,6,1,7] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> ? = 648
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,2,6,1,7] => ([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
=> ? = 540
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=> [6,5,7,2,3,4,1] => [2,3,1,6,5,4,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ? = 1200
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> [5,6,7,2,3,4,1] => [3,2,1,6,5,4,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
=> ? = 1000
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=> [7,6,4,2,3,5,1] => [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
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [7,5,4,2,3,6,1] => [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
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=> [6,4,5,2,3,7,1] => [2,4,3,6,5,1,7] => ([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 768
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=> [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 640
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=> [7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
=> ? = 1008
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=> [6,7,3,2,4,5,1] => [2,1,5,6,4,3,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
=> ? = 864
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> [7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
=> ? = 840
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
=> ? = 720
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ? = 672
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [6,4,3,2,5,7,1] => [2,4,5,6,3,1,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
=> ? = 576
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
Mp00142: Dyck paths —promotion⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 6% ●values known / values provided: 8%●distinct values known / distinct values provided: 6%
Mp00142: Dyck paths —promotion⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 6% ●values known / values provided: 8%●distinct values known / distinct values provided: 6%
Values
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [2,1]
=> 2
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,1,0,0]
=> [1,1]
=> 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 6
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 4
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [3,1,1]
=> 3
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1]
=> 1
[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]
=> [4,3,2,1]
=> 24
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 18
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> 16
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 12
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> 8
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> 12
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> 9
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> 8
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 6
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> 4
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> 4
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> 3
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> 1
[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]
=> [5,4,3,2,1]
=> ? = 120
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? = 96
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? = 90
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> ? = 72
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> 54
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> ? = 80
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> ? = 64
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> ? = 60
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> 48
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 36
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> 40
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> 24
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> 16
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? = 60
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> ? = 48
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> ? = 45
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> 36
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> 27
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> ? = 40
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> 32
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> 30
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> 24
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 18
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> 20
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> 16
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1,1]
=> 12
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,2,2,1,1]
=> 8
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> 20
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> 16
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> 15
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,1,1]
=> 12
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> 9
[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]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,1,1]
=> 8
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,1,1]
=> 6
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,2,1,1,1]
=> 4
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [5,1,1,1,1]
=> 5
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [4,1,1,1,1]
=> 4
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [3,1,1,1,1]
=> 3
[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]
=> [6,5,4,3,2,1]
=> ? = 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]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> ? = 600
[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]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2,1]
=> ? = 576
[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]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,2,1]
=> ? = 480
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,4,4,3,2,1]
=> ? = 384
[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]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> ? = 540
[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]
=> [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> ? = 450
[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]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2,1]
=> ? = 432
[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]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,2,1]
=> ? = 360
[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]
=> [1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,4,3,3,2,1]
=> ? = 288
[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]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,3,3,2,1]
=> ? = 324
[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]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [5,3,3,3,2,1]
=> ? = 270
[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]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [4,3,3,3,2,1]
=> ? = 216
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,3,3,3,2,1]
=> ? = 162
[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]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> ? = 480
[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]
=> [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> ? = 400
[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]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> ? = 384
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> ? = 320
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,2,1]
=> ? = 256
[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]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? = 360
[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]
=> [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> ? = 300
[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]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2,1]
=> ? = 288
[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]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,2,1]
=> ? = 240
[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]
=> [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,2,1]
=> ? = 192
[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]
=> [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,2,1]
=> ? = 216
[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]
=> [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,2,1]
=> ? = 180
[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]
=> [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,2,1]
=> ? = 144
[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]
=> [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2,2,1]
=> ? = 108
[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]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,2,2,1]
=> ? = 240
[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]
=> [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=> [5,5,2,2,2,1]
=> ? = 200
[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]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,2,1]
=> ? = 192
[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]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [5,4,2,2,2,1]
=> ? = 160
[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]
=> [1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,2,1]
=> ? = 128
[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]
=> [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,2,1]
=> ? = 144
[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]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,2,1]
=> ? = 120
[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]
=> [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [4,3,2,2,2,1]
=> ? = 96
[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]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2,2,1]
=> ? = 72
[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]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,2,2,2,1]
=> ? = 96
[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]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [5,2,2,2,2,1]
=> ? = 80
Description
The product of the parts of an integer partition.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!