searching the database
Your data matches 8 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: St000048
St000048: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1
[2]
=> 1
[1,1]
=> 2
[3]
=> 1
[2,1]
=> 3
[1,1,1]
=> 6
[4]
=> 1
[3,1]
=> 4
[2,2]
=> 6
[2,1,1]
=> 12
[1,1,1,1]
=> 24
[5]
=> 1
[4,1]
=> 5
[3,2]
=> 10
[3,1,1]
=> 20
[2,2,1]
=> 30
[2,1,1,1]
=> 60
[1,1,1,1,1]
=> 120
[6]
=> 1
[5,1]
=> 6
[4,2]
=> 15
[4,1,1]
=> 30
[3,3]
=> 20
[3,2,1]
=> 60
[3,1,1,1]
=> 120
[2,2,2]
=> 90
[2,2,1,1]
=> 180
[2,1,1,1,1]
=> 360
[1,1,1,1,1,1]
=> 720
[7]
=> 1
[6,1]
=> 7
[5,2]
=> 21
[5,1,1]
=> 42
[4,3]
=> 35
[4,2,1]
=> 105
[4,1,1,1]
=> 210
[3,3,1]
=> 140
[3,2,2]
=> 210
[3,2,1,1]
=> 420
[3,1,1,1,1]
=> 840
[2,2,2,1]
=> 630
[2,2,1,1,1]
=> 1260
[2,1,1,1,1,1]
=> 2520
[1,1,1,1,1,1,1]
=> 5040
[8]
=> 1
[7,1]
=> 8
[6,2]
=> 28
[6,1,1]
=> 56
[5,3]
=> 56
[5,2,1]
=> 168
Description
The multinomial of the parts of a partition.
Given an integer partition $\lambda = [\lambda_1,\ldots,\lambda_k]$, this is the multinomial
$$\binom{|\lambda|}{\lambda_1,\ldots,\lambda_k}.$$
For any integer composition $\mu$ that is a rearrangement of $\lambda$, this is the number of ordered set partitions whose list of block sizes is $\mu$.
Matching statistic: St000110
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> [[1]]
=> [1] => 1
[2]
=> [[1,2]]
=> [1,2] => 1
[1,1]
=> [[1],[2]]
=> [2,1] => 2
[3]
=> [[1,2,3]]
=> [1,2,3] => 1
[2,1]
=> [[1,2],[3]]
=> [3,1,2] => 3
[1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 6
[4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 1
[3,1]
=> [[1,2,3],[4]]
=> [4,1,2,3] => 4
[2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 6
[2,1,1]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => 12
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => 24
[5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 1
[4,1]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => 5
[3,2]
=> [[1,2,3],[4,5]]
=> [4,5,1,2,3] => 10
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => 20
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [5,3,4,1,2] => 30
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => 60
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => 120
[6]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => 6
[4,2]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => 15
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => 30
[3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 20
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => 60
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => 120
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 90
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => 180
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => 360
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => 720
[7]
=> [[1,2,3,4,5,6,7]]
=> [1,2,3,4,5,6,7] => 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => 7
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [6,7,1,2,3,4,5] => 21
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => 42
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [5,6,7,1,2,3,4] => 35
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [7,5,6,1,2,3,4] => 105
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => 210
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [7,4,5,6,1,2,3] => 140
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [6,7,4,5,1,2,3] => 210
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [7,6,4,5,1,2,3] => 420
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [7,6,5,4,1,2,3] => 840
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [7,5,6,3,4,1,2] => 630
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [7,6,5,3,4,1,2] => 1260
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,1,2] => 2520
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => 5040
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [1,2,3,4,5,6,7,8] => 1
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [8,1,2,3,4,5,6,7] => 8
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [7,8,1,2,3,4,5,6] => 28
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [8,7,1,2,3,4,5,6] => 56
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [6,7,8,1,2,3,4,5] => 56
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [8,6,7,1,2,3,4,5] => 168
Description
The number of permutations less than or equal to a permutation in left weak order.
This is the same as the number of permutations less than or equal to the given permutation in right weak order.
Matching statistic: St000100
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 50% ●values known / values provided: 53%●distinct values known / distinct values provided: 50%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 50% ●values known / values provided: 53%●distinct values known / distinct values provided: 50%
Values
[1]
=> [[1]]
=> [1] => ([],1)
=> ? = 1
[2]
=> [[1,2]]
=> [1,2] => ([(0,1)],2)
=> 1
[1,1]
=> [[1],[2]]
=> [2,1] => ([],2)
=> 2
[3]
=> [[1,2,3]]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[2,1]
=> [[1,2],[3]]
=> [3,1,2] => ([(1,2)],3)
=> 3
[1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => ([],3)
=> 6
[4]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1]
=> [[1,2,3],[4]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> 4
[2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> 6
[2,1,1]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => ([(2,3)],4)
=> 12
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => ([],4)
=> 24
[5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[4,1]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> 5
[3,2]
=> [[1,2,3],[4,5]]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> 10
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> 20
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> 30
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> 60
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => ([],5)
=> 120
[6]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> 6
[4,2]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> 15
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> 30
[3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
=> 20
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
=> 60
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
=> 120
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
=> 90
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
=> 180
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => ([(4,5)],6)
=> 360
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => ([],6)
=> 720
[7]
=> [[1,2,3,4,5,6,7]]
=> [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,1,2] => ([(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => ([],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> 1
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [7,8,1,2,3,4,5,6] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [8,7,1,2,3,4,5,6] => ([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [6,7,8,1,2,3,4,5] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [8,6,7,1,2,3,4,5] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[5,1,1,1]
=> [[1,2,3,4,5],[6],[7],[8]]
=> [8,7,6,1,2,3,4,5] => ([(3,4),(4,7),(6,5),(7,6)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> 70
[4,3,1]
=> [[1,2,3,4],[5,6,7],[8]]
=> [8,5,6,7,1,2,3,4] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[4,2,2]
=> [[1,2,3,4],[5,6],[7,8]]
=> [7,8,5,6,1,2,3,4] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[4,2,1,1]
=> [[1,2,3,4],[5,6],[7],[8]]
=> [8,7,5,6,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[4,1,1,1,1]
=> [[1,2,3,4],[5],[6],[7],[8]]
=> [8,7,6,5,1,2,3,4] => ([(4,5),(5,7),(7,6)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[3,3,2]
=> [[1,2,3],[4,5,6],[7,8]]
=> [7,8,4,5,6,1,2,3] => ([(0,5),(1,7),(2,6),(6,3),(7,4)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[3,3,1,1]
=> [[1,2,3],[4,5,6],[7],[8]]
=> [8,7,4,5,6,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8)
=> 1120
[3,2,2,1]
=> [[1,2,3],[4,5],[6,7],[8]]
=> [8,6,7,4,5,1,2,3] => ([(1,5),(2,4),(3,6),(6,7)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[3,2,1,1,1]
=> [[1,2,3],[4,5],[6],[7],[8]]
=> [8,7,6,4,5,1,2,3] => ([(3,5),(4,6),(6,7)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[3,1,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7],[8]]
=> [8,7,6,5,4,1,2,3] => ([(5,6),(6,7)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[2,2,2,2]
=> [[1,2],[3,4],[5,6],[7,8]]
=> [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8)
=> 2520
[2,2,2,1,1]
=> [[1,2],[3,4],[5,6],[7],[8]]
=> [8,7,5,6,3,4,1,2] => ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[2,2,1,1,1,1]
=> [[1,2],[3,4],[5],[6],[7],[8]]
=> [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8)
=> 10080
[2,1,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7],[8]]
=> [8,7,6,5,4,3,1,2] => ([(6,7)],8)
=> ? ∊ {8,28,56,56,168,280,336,420,560,840,1680,1680,3360,5040,6720,20160}
[1,1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7],[8]]
=> [8,7,6,5,4,3,2,1] => ([],8)
=> 40320
Description
The number of linear extensions of a poset.
Matching statistic: St001855
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 15% ●values known / values provided: 18%●distinct values known / distinct values provided: 15%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 15% ●values known / values provided: 18%●distinct values known / distinct values provided: 15%
Values
[1]
=> [[1]]
=> [1] => [1] => 1
[2]
=> [[1,2]]
=> [1,2] => [1,2] => 1
[1,1]
=> [[1],[2]]
=> [2,1] => [2,1] => 2
[3]
=> [[1,2,3]]
=> [1,2,3] => [1,2,3] => 1
[2,1]
=> [[1,2],[3]]
=> [3,1,2] => [3,1,2] => 3
[1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => [3,2,1] => 6
[4]
=> [[1,2,3,4]]
=> [1,2,3,4] => [1,2,3,4] => 1
[3,1]
=> [[1,2,3],[4]]
=> [4,1,2,3] => [4,1,2,3] => 4
[2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => [3,4,1,2] => 6
[2,1,1]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => [4,3,1,2] => 12
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => [4,3,2,1] => 24
[5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => [1,2,3,4,5] => 1
[4,1]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => [5,1,2,3,4] => ? ∊ {5,10,20,30,60,120}
[3,2]
=> [[1,2,3],[4,5]]
=> [4,5,1,2,3] => [4,5,1,2,3] => ? ∊ {5,10,20,30,60,120}
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => [5,4,1,2,3] => ? ∊ {5,10,20,30,60,120}
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? ∊ {5,10,20,30,60,120}
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => [5,4,3,1,2] => ? ∊ {5,10,20,30,60,120}
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => [5,4,3,2,1] => ? ∊ {5,10,20,30,60,120}
[6]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[5,1]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => [6,1,2,3,4,5] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[4,2]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => [6,5,1,2,3,4] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => [6,4,5,1,2,3] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => [6,5,4,1,2,3] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => [5,6,3,4,1,2] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => [6,5,3,4,1,2] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => [6,5,4,3,1,2] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => ? ∊ {1,6,15,20,30,60,90,120,180,360,720}
[7]
=> [[1,2,3,4,5,6,7]]
=> [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [6,7,1,2,3,4,5] => [6,7,1,2,3,4,5] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [5,6,7,1,2,3,4] => [5,6,7,1,2,3,4] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [7,5,6,1,2,3,4] => [7,5,6,1,2,3,4] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [7,4,5,6,1,2,3] => [7,4,5,6,1,2,3] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [6,7,4,5,1,2,3] => [6,7,4,5,1,2,3] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [7,6,4,5,1,2,3] => [7,6,4,5,1,2,3] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [7,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [7,8,1,2,3,4,5,6] => [7,8,1,2,3,4,5,6] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [8,7,1,2,3,4,5,6] => [8,7,1,2,3,4,5,6] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [6,7,8,1,2,3,4,5] => [6,7,8,1,2,3,4,5] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [8,6,7,1,2,3,4,5] => [8,6,7,1,2,3,4,5] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,1,1,1]
=> [[1,2,3,4,5],[6],[7],[8]]
=> [8,7,6,1,2,3,4,5] => [8,7,6,1,2,3,4,5] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [5,6,7,8,1,2,3,4] => [5,6,7,8,1,2,3,4] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,3,1]
=> [[1,2,3,4],[5,6,7],[8]]
=> [8,5,6,7,1,2,3,4] => [8,5,6,7,1,2,3,4] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,2]
=> [[1,2,3,4],[5,6],[7,8]]
=> [7,8,5,6,1,2,3,4] => [7,8,5,6,1,2,3,4] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,1,1]
=> [[1,2,3,4],[5,6],[7],[8]]
=> [8,7,5,6,1,2,3,4] => [8,7,5,6,1,2,3,4] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,1,1,1,1]
=> [[1,2,3,4],[5],[6],[7],[8]]
=> [8,7,6,5,1,2,3,4] => [8,7,6,5,1,2,3,4] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,3,2]
=> [[1,2,3],[4,5,6],[7,8]]
=> [7,8,4,5,6,1,2,3] => [7,8,4,5,6,1,2,3] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,3,1,1]
=> [[1,2,3],[4,5,6],[7],[8]]
=> [8,7,4,5,6,1,2,3] => [8,7,4,5,6,1,2,3] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,2,2,1]
=> [[1,2,3],[4,5],[6,7],[8]]
=> [8,6,7,4,5,1,2,3] => [8,6,7,4,5,1,2,3] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,2,1,1,1]
=> [[1,2,3],[4,5],[6],[7],[8]]
=> [8,7,6,4,5,1,2,3] => [8,7,6,4,5,1,2,3] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,1,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7],[8]]
=> [8,7,6,5,4,1,2,3] => [8,7,6,5,4,1,2,3] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[2,2,2,2]
=> [[1,2],[3,4],[5,6],[7,8]]
=> [7,8,5,6,3,4,1,2] => [7,8,5,6,3,4,1,2] => ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
Description
The number of signed permutations less than or equal to a signed permutation in left weak order.
Matching statistic: St001645
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 15%
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 15%
Values
[1]
=> [[1]]
=> [1] => ([],1)
=> 1
[2]
=> [[1,2]]
=> [2] => ([],2)
=> ? = 1
[1,1]
=> [[1],[2]]
=> [1,1] => ([(0,1)],2)
=> 2
[3]
=> [[1,2,3]]
=> [3] => ([],3)
=> ? ∊ {1,6}
[2,1]
=> [[1,3],[2]]
=> [1,2] => ([(1,2)],3)
=> ? ∊ {1,6}
[1,1,1]
=> [[1],[2],[3]]
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[4]
=> [[1,2,3,4]]
=> [4] => ([],4)
=> ? ∊ {1,6,12,24}
[3,1]
=> [[1,3,4],[2]]
=> [1,3] => ([(2,3)],4)
=> ? ∊ {1,6,12,24}
[2,2]
=> [[1,2],[3,4]]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {1,6,12,24}
[2,1,1]
=> [[1,4],[2],[3]]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,6,12,24}
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[5]
=> [[1,2,3,4,5]]
=> [5] => ([],5)
=> ? ∊ {1,10,20,30,60,120}
[4,1]
=> [[1,3,4,5],[2]]
=> [1,4] => ([(3,4)],5)
=> ? ∊ {1,10,20,30,60,120}
[3,2]
=> [[1,2,5],[3,4]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {1,10,20,30,60,120}
[3,1,1]
=> [[1,4,5],[2],[3]]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,10,20,30,60,120}
[2,2,1]
=> [[1,3],[2,5],[4]]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,10,20,30,60,120}
[2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,10,20,30,60,120}
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[6]
=> [[1,2,3,4,5,6]]
=> [6] => ([],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[5,1]
=> [[1,3,4,5,6],[2]]
=> [1,5] => ([(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[4,2]
=> [[1,2,5,6],[3,4]]
=> [2,4] => ([(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[4,1,1]
=> [[1,4,5,6],[2],[3]]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,3]
=> [[1,2,3],[4,5,6]]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,2,1]
=> [[1,3,6],[2,5],[4]]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[7]
=> [[1,2,3,4,5,6,7]]
=> [7] => ([],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[6,1]
=> [[1,3,4,5,6,7],[2]]
=> [1,6] => ([(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [[1,2,5,6,7],[3,4]]
=> [2,5] => ([(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [[1,4,5,6,7],[2],[3]]
=> [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [[1,2,3,7],[4,5,6]]
=> [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [[1,3,6,7],[2,5],[4]]
=> [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [[1,3,4],[2,6,7],[5]]
=> [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [[1,2,7],[3,4],[5,6]]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [[1,3],[2,5],[4,7],[6]]
=> [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [[1,5],[2,7],[3],[4],[6]]
=> [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [8] => ([],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[7,1]
=> [[1,3,4,5,6,7,8],[2]]
=> [1,7] => ([(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,2]
=> [[1,2,5,6,7,8],[3,4]]
=> [2,6] => ([(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,1,1]
=> [[1,4,5,6,7,8],[2],[3]]
=> [1,1,6] => ([(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,3]
=> [[1,2,3,7,8],[4,5,6]]
=> [3,5] => ([(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,2,1]
=> [[1,3,6,7,8],[2,5],[4]]
=> [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,1,1,1]
=> [[1,5,6,7,8],[2],[3],[4]]
=> [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,3,1]
=> [[1,3,4,8],[2,6,7],[5]]
=> [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,2]
=> [[1,2,7,8],[3,4],[5,6]]
=> [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,1,1]
=> [[1,4,7,8],[2,6],[3],[5]]
=> [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,1,1,1,1]
=> [[1,6,7,8],[2],[3],[4],[5]]
=> [1,1,1,1,4] => ([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[3,3,2]
=> [[1,2,5],[3,4,8],[6,7]]
=> [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
Description
The pebbling number of a connected graph.
Matching statistic: St000456
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 13%
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 13%
Values
[1]
=> [[1]]
=> [1] => ([],1)
=> ? = 1
[2]
=> [[1,2]]
=> [2] => ([],2)
=> ? = 2
[1,1]
=> [[1],[2]]
=> [1,1] => ([(0,1)],2)
=> 1
[3]
=> [[1,2,3]]
=> [3] => ([],3)
=> ? ∊ {1,6}
[2,1]
=> [[1,3],[2]]
=> [1,2] => ([(1,2)],3)
=> ? ∊ {1,6}
[1,1,1]
=> [[1],[2],[3]]
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
[4]
=> [[1,2,3,4]]
=> [4] => ([],4)
=> ? ∊ {1,4,12,24}
[3,1]
=> [[1,3,4],[2]]
=> [1,3] => ([(2,3)],4)
=> ? ∊ {1,4,12,24}
[2,2]
=> [[1,2],[3,4]]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {1,4,12,24}
[2,1,1]
=> [[1,4],[2],[3]]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,4,12,24}
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[5]
=> [[1,2,3,4,5]]
=> [5] => ([],5)
=> ? ∊ {1,5,20,30,60,120}
[4,1]
=> [[1,3,4,5],[2]]
=> [1,4] => ([(3,4)],5)
=> ? ∊ {1,5,20,30,60,120}
[3,2]
=> [[1,2,5],[3,4]]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {1,5,20,30,60,120}
[3,1,1]
=> [[1,4,5],[2],[3]]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,5,20,30,60,120}
[2,2,1]
=> [[1,3],[2,5],[4]]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,5,20,30,60,120}
[2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,5,20,30,60,120}
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 10
[6]
=> [[1,2,3,4,5,6]]
=> [6] => ([],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[5,1]
=> [[1,3,4,5,6],[2]]
=> [1,5] => ([(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[4,2]
=> [[1,2,5,6],[3,4]]
=> [2,4] => ([(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[4,1,1]
=> [[1,4,5,6],[2],[3]]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[3,3]
=> [[1,2,3],[4,5,6]]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[3,2,1]
=> [[1,3,6],[2,5],[4]]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,6,20,30,60,90,120,180,360,720}
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 15
[7]
=> [[1,2,3,4,5,6,7]]
=> [7] => ([],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[6,1]
=> [[1,3,4,5,6,7],[2]]
=> [1,6] => ([(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [[1,2,5,6,7],[3,4]]
=> [2,5] => ([(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [[1,4,5,6,7],[2],[3]]
=> [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [[1,2,3,7],[4,5,6]]
=> [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [[1,3,6,7],[2,5],[4]]
=> [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [[1,3,4],[2,6,7],[5]]
=> [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [[1,2,7],[3,4],[5,6]]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [[1,3],[2,5],[4,7],[6]]
=> [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [[1,5],[2,7],[3],[4],[6]]
=> [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,7,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 21
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [8] => ([],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[7,1]
=> [[1,3,4,5,6,7,8],[2]]
=> [1,7] => ([(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,2]
=> [[1,2,5,6,7,8],[3,4]]
=> [2,6] => ([(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,1,1]
=> [[1,4,5,6,7,8],[2],[3]]
=> [1,1,6] => ([(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,3]
=> [[1,2,3,7,8],[4,5,6]]
=> [3,5] => ([(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,2,1]
=> [[1,3,6,7,8],[2,5],[4]]
=> [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,1,1,1]
=> [[1,5,6,7,8],[2],[3],[4]]
=> [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,3,1]
=> [[1,3,4,8],[2,6,7],[5]]
=> [1,3,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,2]
=> [[1,2,7,8],[3,4],[5,6]]
=> [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,1,1]
=> [[1,4,7,8],[2,6],[3],[5]]
=> [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,1,1,1,1]
=> [[1,6,7,8],[2],[3],[4],[5]]
=> [1,1,1,1,4] => ([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St001232
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 13%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 13%
Values
[1]
=> [1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[2]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 2
[1,1]
=> [1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 1
[3]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[2,1]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {1,6}
[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]
=> ? ∊ {1,6}
[4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {1,6,12,24}
[2,2]
=> [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {1,6,12,24}
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {1,6,12,24}
[1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {1,6,12,24}
[5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {1,10,20,30,60,120}
[3,2]
=> [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]
=> ? ∊ {1,10,20,30,60,120}
[3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> ? ∊ {1,10,20,30,60,120}
[2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {1,10,20,30,60,120}
[2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ? ∊ {1,10,20,30,60,120}
[1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? ∊ {1,10,20,30,60,120}
[6]
=> [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]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
[5,1]
=> [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]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[4,1,1]
=> [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]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,3]
=> [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]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[3,1,1,1]
=> [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]
=> [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,2,2]
=> [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]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[2,1,1,1,1]
=> [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]
=> [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,15,20,30,60,90,120,180,360,720}
[7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [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]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [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]
=> [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [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]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [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]
=> [1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[7,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,3]
=> [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]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,3,1]
=> [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]
=> [1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,2]
=> [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]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001632
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 9%●distinct values known / distinct values provided: 2%
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 9%●distinct values known / distinct values provided: 2%
Values
[1]
=> [[1]]
=> [1] => ([],1)
=> ? = 1
[2]
=> [[1,2]]
=> [1,2] => ([(0,1)],2)
=> 1
[1,1]
=> [[1],[2]]
=> [2,1] => ([],2)
=> ? = 2
[3]
=> [[1,2,3]]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[2,1]
=> [[1,2],[3]]
=> [3,1,2] => ([(1,2)],3)
=> ? ∊ {3,6}
[1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => ([],3)
=> ? ∊ {3,6}
[4]
=> [[1,2,3,4]]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[3,1]
=> [[1,2,3],[4]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? ∊ {4,6,12,24}
[2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ? ∊ {4,6,12,24}
[2,1,1]
=> [[1,2],[3],[4]]
=> [4,3,1,2] => ([(2,3)],4)
=> ? ∊ {4,6,12,24}
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => ([],4)
=> ? ∊ {4,6,12,24}
[5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[4,1]
=> [[1,2,3,4],[5]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ? ∊ {5,10,20,30,60,120}
[3,2]
=> [[1,2,3],[4,5]]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ? ∊ {5,10,20,30,60,120}
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> ? ∊ {5,10,20,30,60,120}
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> ? ∊ {5,10,20,30,60,120}
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> ? ∊ {5,10,20,30,60,120}
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => ([],5)
=> ? ∊ {5,10,20,30,60,120}
[6]
=> [[1,2,3,4,5,6]]
=> [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[4,2]
=> [[1,2,3,4],[5,6]]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [6,5,4,3,1,2] => ([(4,5)],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => ([],6)
=> ? ∊ {6,15,20,30,60,90,120,180,360,720}
[7]
=> [[1,2,3,4,5,6,7]]
=> [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,1,2] => ([(5,6)],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => ([],7)
=> ? ∊ {7,21,35,42,105,140,210,210,420,630,840,1260,2520,5040}
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [7,8,1,2,3,4,5,6] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [8,7,1,2,3,4,5,6] => ([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [6,7,8,1,2,3,4,5] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [8,6,7,1,2,3,4,5] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[5,1,1,1]
=> [[1,2,3,4,5],[6],[7],[8]]
=> [8,7,6,1,2,3,4,5] => ([(3,4),(4,7),(6,5),(7,6)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,4]
=> [[1,2,3,4],[5,6,7,8]]
=> [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,3,1]
=> [[1,2,3,4],[5,6,7],[8]]
=> [8,5,6,7,1,2,3,4] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,2]
=> [[1,2,3,4],[5,6],[7,8]]
=> [7,8,5,6,1,2,3,4] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,2,1,1]
=> [[1,2,3,4],[5,6],[7],[8]]
=> [8,7,5,6,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
[4,1,1,1,1]
=> [[1,2,3,4],[5],[6],[7],[8]]
=> [8,7,6,5,1,2,3,4] => ([(4,5),(5,7),(7,6)],8)
=> ? ∊ {1,8,28,56,56,70,168,280,336,420,560,840,1120,1680,1680,2520,3360,5040,6720,10080,20160,40320}
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
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!