Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000957
(load all 5 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
St000957: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => 1
{{1},{2}}
 => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => 2
{{1,2},{3}}
 => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => 2
{{1},{2,3}}
 => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => 4
{{1},{2,4},{3}}
 => [1,4,3,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => 4
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => 4
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => 3
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => 2
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => 4
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => 5
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => 3
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => 4
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => 3
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => 2
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => 5
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => 3
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => 2
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => 1
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => 4
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => 5
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => 3
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => 4
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => 5
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => 4
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => 4
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => 5
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => 3
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => 2
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => 4
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => 5
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => 3
Description
The number of Bruhat lower covers of a permutation. This is, for a permutation $\pi$, the number of permutations $\tau$ with $\operatorname{inv}(\tau) = \operatorname{inv}(\pi) - 1$ such that $\tau*t = \pi$ for a transposition $t$. This is also the number of occurrences of the boxed pattern $21$: occurrences of the pattern $21$ such that any entry between the two matched entries is either larger or smaller than both of the matched entries.
Matching statistic: St000327
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000327: Posets ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 70%
Values
{{1,2}}
 => [2,1] => [1,2] => ([(0,1)],2)
 => 1
{{1},{2}}
 => [1,2] => [2,1] => ([],2)
 => 0
{{1,2,3}}
 => [2,3,1] => [1,3,2] => ([(0,1),(0,2)],3)
 => 2
{{1,2},{3}}
 => [2,1,3] => [3,1,2] => ([(1,2)],3)
 => 1
{{1,3},{2}}
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
{{1},{2,3}}
 => [1,3,2] => [2,3,1] => ([(1,2)],3)
 => 1
{{1},{2},{3}}
 => [1,2,3] => [3,2,1] => ([],3)
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [4,1,3,2] => ([(1,2),(1,3)],4)
 => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [3,4,1,2] => ([(0,3),(1,2)],4)
 => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [4,3,1,2] => ([(2,3)],4)
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
 => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [4,2,3,1] => ([(2,3)],4)
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
{{1},{2,4},{3}}
 => [1,4,3,2] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [3,4,2,1] => ([(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [4,3,2,1] => ([],4)
 => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 4
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
 => 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 4
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
 => 3
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [5,4,1,3,2] => ([(2,3),(2,4)],5)
 => 2
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 4
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [3,1,5,4,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 5
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [5,1,3,4,2] => ([(1,3),(1,4),(4,2)],5)
 => 3
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
 => 3
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => 2
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 5
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => 3
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [4,5,3,1,2] => ([(1,4),(2,3)],5)
 => 2
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [5,4,3,1,2] => ([(3,4)],5)
 => 1
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 4
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 5
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [5,1,4,2,3] => ([(1,3),(1,4),(4,2)],5)
 => 3
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 4
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [2,5,1,4,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 5
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [5,2,1,4,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 4
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => 5
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => 3
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => 2
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 5
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => 3
{{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ? = 5
{{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
 => ? = 4
{{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => [1,5,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ? = 5
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [5,6,1,4,3,2] => ([(0,5),(1,2),(1,3),(1,4)],6)
 => ? = 4
{{1,2,3,4},{5},{6}}
 => [2,3,4,1,5,6] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6)
 => ? = 3
{{1,2,3,5,6},{4}}
 => [2,3,5,4,6,1] => [1,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ? = 5
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => [4,1,6,5,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => ? = 6
{{1,2,3,5},{4},{6}}
 => [2,3,5,4,1,6] => [6,1,4,5,3,2] => ([(1,3),(1,4),(1,5),(5,2)],6)
 => ? = 4
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [1,4,5,6,3,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => ? = 5
{{1,2,3},{4,5,6}}
 => [2,3,1,5,6,4] => [4,6,5,1,3,2] => ([(0,4),(0,5),(1,2),(1,3)],6)
 => ? = 4
{{1,2,3},{4,5},{6}}
 => [2,3,1,5,4,6] => [6,4,5,1,3,2] => ([(1,5),(2,3),(2,4)],6)
 => ? = 3
{{1,2,3,6},{4},{5}}
 => [2,3,6,4,5,1] => [1,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ? = 6
{{1,2,3},{4,6},{5}}
 => [2,3,1,6,5,4] => [4,5,6,1,3,2] => ([(0,5),(1,3),(1,4),(5,2)],6)
 => ? = 4
{{1,2,3},{4},{5,6}}
 => [2,3,1,4,6,5] => [5,6,4,1,3,2] => ([(1,5),(2,3),(2,4)],6)
 => ? = 3
{{1,2,3},{4},{5},{6}}
 => [2,3,1,4,5,6] => [6,5,4,1,3,2] => ([(3,4),(3,5)],6)
 => ? = 2
{{1,2,4,5,6},{3}}
 => [2,4,3,5,6,1] => [1,6,5,3,4,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ? = 5
{{1,2,4,5},{3,6}}
 => [2,4,6,5,1,3] => [3,1,5,6,4,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ? = 6
{{1,2,4,5},{3},{6}}
 => [2,4,3,5,1,6] => [6,1,5,3,4,2] => ([(1,3),(1,4),(1,5),(5,2)],6)
 => ? = 4
{{1,2,4,6},{3,5}}
 => [2,4,5,6,3,1] => [1,3,6,5,4,2] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ? = 5
{{1,2,4},{3,5,6}}
 => [2,4,5,1,6,3] => [3,6,1,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
 => ? = 6
{{1,2,4},{3,5},{6}}
 => [2,4,5,1,3,6] => [6,3,1,5,4,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ? = 5
{{1,2,4,6},{3},{5}}
 => [2,4,3,6,5,1] => [1,5,6,3,4,2] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ? = 5
{{1,2,4},{3,6},{5}}
 => [2,4,6,1,5,3] => [3,5,1,6,4,2] => ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)
 => ? = 6
{{1,2,4},{3},{5,6}}
 => [2,4,3,1,6,5] => [5,6,1,3,4,2] => ([(0,4),(1,3),(1,5),(5,2)],6)
 => ? = 4
{{1,2,4},{3},{5},{6}}
 => [2,4,3,1,5,6] => [6,5,1,3,4,2] => ([(2,3),(2,4),(4,5)],6)
 => ? = 3
{{1,2,5,6},{3,4}}
 => [2,5,4,3,6,1] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => ? = 5
{{1,2,5},{3,4,6}}
 => [2,5,4,6,1,3] => [3,1,6,4,5,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ? = 6
{{1,2,5},{3,4},{6}}
 => [2,5,4,3,1,6] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6)
 => ? = 4
{{1,2,6},{3,4,5}}
 => [2,6,4,5,3,1] => [1,3,5,4,6,2] => ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
 => ? = 6
{{1,2},{3,4,5,6}}
 => [2,1,4,5,6,3] => [3,6,5,4,1,2] => ([(0,5),(1,2),(1,3),(1,4)],6)
 => ? = 4
{{1,2},{3,4,5},{6}}
 => [2,1,4,5,3,6] => [6,3,5,4,1,2] => ([(1,5),(2,3),(2,4)],6)
 => ? = 3
{{1,2,6},{3,4},{5}}
 => [2,6,4,3,5,1] => [1,5,3,4,6,2] => ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
 => ? = 6
{{1,2},{3,4,6},{5}}
 => [2,1,4,6,5,3] => [3,5,6,4,1,2] => ([(0,4),(1,3),(1,5),(5,2)],6)
 => ? = 4
{{1,2},{3,4},{5,6}}
 => [2,1,4,3,6,5] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
 => ? = 3
{{1,2},{3,4},{5},{6}}
 => [2,1,4,3,5,6] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
 => ? = 2
{{1,2,5,6},{3},{4}}
 => [2,5,3,4,6,1] => [1,6,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ? = 6
{{1,2,5},{3,6},{4}}
 => [2,5,6,4,1,3] => [3,1,4,6,5,2] => ([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
 => ? = 5
{{1,2,5},{3},{4,6}}
 => [2,5,3,6,1,4] => [4,1,6,3,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
 => ? = 6
{{1,2,5},{3},{4},{6}}
 => [2,5,3,4,1,6] => [6,1,4,3,5,2] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ? = 5
{{1,2,6},{3,5},{4}}
 => [2,6,5,4,3,1] => [1,3,4,5,6,2] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ? = 5
{{1,2},{3,5,6},{4}}
 => [2,1,5,4,6,3] => [3,6,4,5,1,2] => ([(0,4),(1,3),(1,5),(5,2)],6)
 => ? = 4
{{1,2},{3,5},{4,6}}
 => [2,1,5,6,3,4] => [4,3,6,5,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => ? = 5
{{1,2},{3,5},{4},{6}}
 => [2,1,5,4,3,6] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6)
 => ? = 3
{{1,2,6},{3},{4,5}}
 => [2,6,3,5,4,1] => [1,4,5,3,6,2] => ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
 => ? = 6
{{1,2},{3,6},{4,5}}
 => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
 => ? = 4
{{1,2},{3},{4,5,6}}
 => [2,1,3,5,6,4] => [4,6,5,3,1,2] => ([(1,5),(2,3),(2,4)],6)
 => ? = 3
{{1,2},{3},{4,5},{6}}
 => [2,1,3,5,4,6] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6)
 => ? = 2
{{1,2,6},{3},{4},{5}}
 => [2,6,3,4,5,1] => [1,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ? = 7
{{1,2},{3,6},{4},{5}}
 => [2,1,6,4,5,3] => [3,5,4,6,1,2] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6)
 => ? = 5
{{1,2},{3},{4,6},{5}}
 => [2,1,3,6,5,4] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6)
 => ? = 3
Description
The number of cover relations in a poset. Equivalently, this is also the number of edges in the Hasse diagram [1].
Matching statistic: St001861
(load all 3 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001861: Signed permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 50%
Values
{{1,2}}
 => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [2,3,1] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [2,4,3,1] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [3,2,4,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,3,4,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 4
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [2,3,4,5,1] => ? = 4
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [2,3,5,4,1] => ? = 4
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [2,3,1,5,4] => ? = 3
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [2,3,1,4,5] => ? = 2
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [2,4,3,5,1] => ? = 4
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [2,4,5,1,3] => ? = 5
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [2,4,3,1,5] => ? = 3
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [2,5,4,3,1] => ? = 4
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [2,1,4,5,3] => ? = 3
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [2,1,4,3,5] => ? = 2
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [2,5,3,4,1] => ? = 5
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [2,1,5,4,3] => ? = 3
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [2,1,3,5,4] => ? = 2
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [2,1,3,4,5] => ? = 1
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [3,2,4,5,1] => ? = 4
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [3,5,4,1,2] => ? = 5
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [3,2,4,1,5] => ? = 3
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [3,4,5,2,1] => ? = 4
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [3,4,1,5,2] => ? = 5
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [3,4,1,2,5] => ? = 4
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [3,2,5,4,1] => ? = 4
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [3,5,1,4,2] => ? = 5
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [3,2,1,5,4] => ? = 3
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [3,2,1,4,5] => ? = 2
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [4,3,2,5,1] => ? = 4
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [4,3,5,1,2] => ? = 5
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [4,3,2,1,5] => ? = 3
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [5,3,4,2,1] => ? = 5
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,3,4,5,2] => 3
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,3,4,2,5] => 2
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [5,3,2,4,1] => ? = 5
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,3,5,4,2] => 3
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => 2
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [4,2,3,5,1] => ? = 5
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [4,5,3,1,2] => ? = 4
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [4,2,5,1,3] => ? = 5
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [4,2,3,1,5] => ? = 4
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,4,3,5,2] => 3
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => 4
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => 2
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [5,2,4,3,1] => ? = 5
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,5,4,3,2] => 3
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,4,5,3] => 2
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [5,2,3,4,1] => ? = 6
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,5,3,4,2] => 4
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => 1
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ? = 5
{{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ? = 4
{{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => [2,3,4,6,5,1] => ? = 5
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [2,3,4,1,6,5] => ? = 4
{{1,2,3,4},{5},{6}}
 => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ? = 3
{{1,2,3,5,6},{4}}
 => [2,3,5,4,6,1] => [2,3,5,4,6,1] => ? = 5
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => [2,3,5,6,1,4] => ? = 6
{{1,2,3,5},{4},{6}}
 => [2,3,5,4,1,6] => [2,3,5,4,1,6] => ? = 4
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [2,3,6,5,4,1] => ? = 5
{{1,2,3},{4,5,6}}
 => [2,3,1,5,6,4] => [2,3,1,5,6,4] => ? = 4
{{1,2,3},{4,5},{6}}
 => [2,3,1,5,4,6] => [2,3,1,5,4,6] => ? = 3
{{1,2,3,6},{4},{5}}
 => [2,3,6,4,5,1] => [2,3,6,4,5,1] => ? = 6
{{1,2,3},{4,6},{5}}
 => [2,3,1,6,5,4] => [2,3,1,6,5,4] => ? = 4
Description
The number of Bruhat lower covers of a permutation. This is, for a signed permutation $\pi$, the number of signed permutations $\tau$ having a reduced word which is obtained by deleting a letter from a reduced word from $\pi$.