Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000454
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => ([],1)
 => 0
{{1,2}}
 => [2,1] => [1,2] => ([],2)
 => 0
{{1},{2}}
 => [1,2] => [2,1] => ([(0,1)],2)
 => 1
{{1,2},{3}}
 => [2,1,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
{{1,3},{2}}
 => [3,2,1] => [1,2,3] => ([],3)
 => 0
{{1},{2,3}}
 => [1,3,2] => [2,1,3] => ([(1,2)],3)
 => 1
{{1,2,3,4}}
 => [2,3,4,1] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
{{1,2},{3,4}}
 => [2,1,4,3] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [1,2,3,4] => ([],4)
 => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [2,1,3,4] => ([(2,3)],4)
 => 1
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
 => 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [1,2,3,4,5] => ([],5)
 => 0
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [2,1,3,4,5] => ([(3,4)],5)
 => 1
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 2
{{1,2},{3,6},{4,5}}
 => [2,1,6,5,4,3] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6)
 => 2
{{1,2},{3,6},{4},{5}}
 => [2,1,6,4,5,3] => [3,2,1,6,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => 2
{{1,3},{2},{4,6},{5}}
 => [3,2,1,6,5,4] => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1,4},{2,3},{5,6}}
 => [4,3,2,1,6,5] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
{{1,5},{2,4},{3},{6}}
 => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(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)
 => 5
{{1,6},{2,4,5},{3}}
 => [6,4,3,5,2,1] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
{{1,6},{2,5},{3,4}}
 => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([],6)
 => 0
{{1},{2,6},{3,5},{4}}
 => [1,6,5,4,3,2] => [2,1,3,4,5,6] => ([(4,5)],6)
 => 1
{{1,6},{2},{3},{4,5}}
 => [6,2,3,5,4,1] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 2
{{1},{2,6},{3},{4},{5}}
 => [1,6,3,4,5,2] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
{{1},{2},{3},{4},{5,6}}
 => [1,2,3,4,6,5] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
{{1,2,3,4},{5,7},{6}}
 => [2,3,4,1,7,6,5] => [3,4,5,2,1,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
{{1,2,3,6,7},{4,5}}
 => [2,3,6,5,4,7,1] => [3,4,7,6,5,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 4
{{1,2,3,7},{4,6},{5}}
 => [2,3,7,6,5,4,1] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
 => 2
{{1,2,5,6,7},{3,4}}
 => [2,5,4,3,6,7,1] => [3,6,5,4,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 4
{{1,2},{3,4},{5,6},{7}}
 => [2,1,4,3,6,5,7] => [3,2,5,4,7,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 3
{{1,2},{3,7},{4,5,6}}
 => [2,1,7,5,6,4,3] => [3,2,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => 2
{{1,2},{3,7},{4,6},{5}}
 => [2,1,7,6,5,4,3] => [3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7)
 => 2
{{1,2},{3,7},{4},{5,6}}
 => [2,1,7,4,6,5,3] => [3,2,1,6,4,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => 2
{{1,2},{3,7},{4},{5},{6}}
 => [2,1,7,4,5,6,3] => [3,2,1,6,7,4,5] => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => 2
{{1,3,7},{2},{4,5},{6}}
 => [3,2,7,5,4,6,1] => [4,3,1,7,6,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
{{1,3,6},{2},{4,7},{5}}
 => [3,2,6,7,5,1,4] => [4,3,7,1,2,6,5] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => 3
{{1,3},{2},{4,7},{5,6}}
 => [3,2,1,7,6,5,4] => [4,3,2,1,5,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
{{1,3},{2},{4,7},{5},{6}}
 => [3,2,1,7,5,6,4] => [4,3,2,1,7,5,6] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
{{1,4,5,6,7},{2,3}}
 => [4,3,2,5,6,7,1] => [5,4,3,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => 4
{{1,4,5,7},{2,3,6}}
 => [4,3,6,5,7,2,1] => [5,4,7,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => 4
{{1,4,6},{2,3,7},{5}}
 => [4,3,7,6,5,1,2] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
{{1,4},{2,3},{5,7},{6}}
 => [4,3,2,1,7,6,5] => [5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 4
Description
The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St001207
(load all 21 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 57%
Values
{{1}}
 => [1] => [1] => [1] => ? = 0
{{1,2}}
 => [2,1] => [2,1] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => [2,1] => 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,3,1] => 2
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [1,2,3] => 0
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => [1,3,2] => 1
{{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => [3,2,1,4] => 2
{{1,2},{3,4}}
 => [2,1,4,3] => [4,2,1,3] => [1,3,4,2] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [2,3,4,1] => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [1,2,3,4] => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,3,1,2] => [1,2,4,3] => 1
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [2,3,4,1,5] => [4,3,2,5,1] => ? = 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [5,2,3,4,1] => [1,4,3,2,5] => ? = 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [5,4,2,1,3] => [1,2,4,5,3] => ? = 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [5,3,2,1,4] => [1,3,4,5,2] => ? = 3
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [4,3,2,1,5] => [2,3,4,5,1] => ? = 4
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ? = 0
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [5,4,3,1,2] => [1,2,3,5,4] => ? = 1
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [2,3,5,4,1] => [4,3,1,2,5] => ? = 2
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 2
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [6,2,3,4,1,5] => [1,5,4,3,6,2] => ? = 3
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [1,2,5,4,3,6] => ? = 2
{{1,2},{3,6},{4,5}}
 => [2,1,6,5,4,3] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => ? = 2
{{1,2},{3,6},{4},{5}}
 => [2,1,6,4,5,3] => [6,2,4,1,5,3] => [1,5,3,6,2,4] => ? = 2
{{1,3},{2},{4,6},{5}}
 => [3,2,1,6,5,4] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => ? = 3
{{1,4},{2,3},{5,6}}
 => [4,3,2,1,6,5] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => ? = 4
{{1,5},{2,4},{3},{6}}
 => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => ? = 5
{{1,6},{2,4,5},{3}}
 => [6,4,3,5,2,1] => [4,6,3,5,2,1] => [3,1,4,2,5,6] => ? = 3
{{1,6},{2,5},{3,4}}
 => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ? = 0
{{1},{2,6},{3,5},{4}}
 => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => ? = 1
{{1,6},{2},{3},{4,5}}
 => [6,2,3,5,4,1] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => ? = 2
{{1},{2,6},{3},{4},{5}}
 => [1,6,3,4,5,2] => [3,1,6,4,5,2] => [4,6,1,3,2,5] => ? = 2
{{1},{2},{3},{4},{5,6}}
 => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => ? = 2
{{1,2,3,4},{5,7},{6}}
 => [2,3,4,1,7,6,5] => [7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => ? = 3
{{1,2,3,6,7},{4,5}}
 => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => ? = 4
{{1,2,3,7},{4,6},{5}}
 => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => ? = 2
{{1,2,5,6,7},{3,4}}
 => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => ? = 4
{{1,2},{3,4},{5,6},{7}}
 => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => [2,4,6,7,5,3,1] => ? = 3
{{1,2},{3,7},{4,5,6}}
 => [2,1,7,5,6,4,3] => [7,5,2,6,1,4,3] => [1,3,6,2,7,4,5] => ? = 2
{{1,2},{3,7},{4,6},{5}}
 => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => ? = 2
{{1,2},{3,7},{4},{5,6}}
 => [2,1,7,4,6,5,3] => [7,6,2,4,1,5,3] => [1,2,6,4,7,3,5] => ? = 2
{{1,2},{3,7},{4},{5},{6}}
 => [2,1,7,4,5,6,3] => [7,2,1,4,5,6,3] => [1,6,7,4,3,2,5] => ? = 2
{{1,3,7},{2},{4,5},{6}}
 => [3,2,7,5,4,6,1] => [5,7,3,2,4,6,1] => [3,1,5,6,4,2,7] => ? = 3
{{1,3,6},{2},{4,7},{5}}
 => [3,2,6,7,5,1,4] => [3,6,2,1,7,5,4] => [5,2,6,7,1,3,4] => ? = 3
{{1,3},{2},{4,7},{5,6}}
 => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => ? = 3
{{1,3},{2},{4,7},{5},{6}}
 => [3,2,1,7,5,6,4] => [7,3,5,2,1,6,4] => [1,5,3,6,7,2,4] => ? = 3
{{1,4,5,6,7},{2,3}}
 => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => ? = 4
{{1,4,5,7},{2,3,6}}
 => [4,3,6,5,7,2,1] => [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => ? = 4
{{1,4,6},{2,3,7},{5}}
 => [4,3,7,6,5,1,2] => [1,7,6,4,3,5,2] => [7,1,2,4,5,3,6] => ? = 3
{{1,4},{2,3},{5,7},{6}}
 => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => ? = 4
{{1,7},{2,3,4,5,6}}
 => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [5,4,3,1,2,6,7] => ? = 3
{{1,6},{2,3},{4,5},{7}}
 => [6,3,2,5,4,1,7] => [6,3,5,2,4,1,7] => [2,5,3,6,4,7,1] => ? = 5
{{1,4},{2,7},{3,5,6}}
 => [4,7,5,1,6,3,2] => [4,7,5,6,3,1,2] => [4,1,3,2,5,7,6] => ? = 3
{{1,5},{2,4},{3},{6,7}}
 => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => ? = 5
{{1,7},{2,4},{3,5},{6}}
 => [7,4,5,2,3,6,1] => [2,4,5,7,3,6,1] => [6,4,3,1,5,2,7] => ? = 4
{{1,7},{2,4,6},{3},{5}}
 => [7,4,3,6,5,2,1] => [7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => ? = 3
{{1,6},{2,5},{3,4},{7}}
 => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [2,3,4,5,6,7,1] => ? = 6
{{1,7},{2,6},{3,4,5}}
 => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [4,1,2,3,5,6,7] => ? = 2
{{1,7},{2,6},{3,4},{5}}
 => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [4,1,2,5,3,6,7] => ? = 3
{{1,7},{2,6},{3,5},{4}}
 => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ? = 0
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St001583
(load all 5 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 57%
Values
{{1}}
 => [1] => [1] => [1] => ? = 0
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 2
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [3,2,1] => 0
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [3,1,2] => 1
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => [2,4,3,1] => 2
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [4,2,1,3] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 1
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [4,2,3,1,5] => [2,4,3,1,5] => ? = 3
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [2,1,5,4,3] => [5,4,2,1,3] => ? = 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [3,2,1,5,4] => [5,3,2,1,4] => ? = 3
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 4
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => ? = 1
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 2
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 2
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [6,2,4,3,1,5] => ? = 3
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [6,2,5,4,3,1] => [6,5,2,4,3,1] => ? = 2
{{1,2},{3,6},{4,5}}
 => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => ? = 2
{{1,2},{3,6},{4},{5}}
 => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [6,5,4,2,1,3] => ? = 2
{{1,3},{2},{4,6},{5}}
 => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [6,5,3,2,1,4] => ? = 3
{{1,4},{2,3},{5,6}}
 => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [6,4,3,2,1,5] => ? = 4
{{1,5},{2,4},{3},{6}}
 => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => ? = 5
{{1,6},{2,4,5},{3}}
 => [6,4,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ? = 3
{{1,6},{2,5},{3,4}}
 => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ? = 0
{{1},{2,6},{3,5},{4}}
 => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ? = 1
{{1,6},{2},{3},{4,5}}
 => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [3,6,5,4,2,1] => ? = 2
{{1},{2,6},{3},{4},{5}}
 => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ? = 2
{{1},{2},{3},{4},{5,6}}
 => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => ? = 2
{{1,2,3,4},{5,7},{6}}
 => [2,3,4,1,7,6,5] => [4,2,3,1,7,6,5] => [7,6,2,4,3,1,5] => ? = 3
{{1,2,3,6,7},{4,5}}
 => [2,3,6,5,4,7,1] => [7,2,5,4,3,6,1] => [5,7,2,4,3,6,1] => ? = 4
{{1,2,3,7},{4,6},{5}}
 => [2,3,7,6,5,4,1] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => ? = 2
{{1,2,5,6,7},{3,4}}
 => [2,5,4,3,6,7,1] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => ? = 4
{{1,2},{3,4},{5,6},{7}}
 => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [6,4,2,1,3,5,7] => ? = 3
{{1,2},{3,7},{4,5,6}}
 => [2,1,7,5,6,4,3] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => ? = 2
{{1,2},{3,7},{4,6},{5}}
 => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => ? = 2
{{1,2},{3,7},{4},{5,6}}
 => [2,1,7,4,6,5,3] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => ? = 2
{{1,2},{3,7},{4},{5},{6}}
 => [2,1,7,4,5,6,3] => [2,1,7,6,5,4,3] => [7,6,5,4,2,1,3] => ? = 2
{{1,3,7},{2},{4,5},{6}}
 => [3,2,7,5,4,6,1] => [7,2,6,5,4,3,1] => [7,6,5,2,4,3,1] => ? = 3
{{1,3,6},{2},{4,7},{5}}
 => [3,2,6,7,5,1,4] => [6,2,7,5,4,1,3] => [2,6,7,5,1,4,3] => ? = 3
{{1,3},{2},{4,7},{5,6}}
 => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => ? = 3
{{1,3},{2},{4,7},{5},{6}}
 => [3,2,1,7,5,6,4] => [3,2,1,7,6,5,4] => [7,6,5,3,2,1,4] => ? = 3
{{1,4,5,6,7},{2,3}}
 => [4,3,2,5,6,7,1] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => ? = 4
{{1,4,5,7},{2,3,6}}
 => [4,3,6,5,7,2,1] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => ? = 4
{{1,4,6},{2,3,7},{5}}
 => [4,3,7,6,5,1,2] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 3
{{1,4},{2,3},{5,7},{6}}
 => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [7,6,4,3,2,1,5] => ? = 4
{{1,7},{2,3,4,5,6}}
 => [7,3,4,5,6,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 3
{{1,6},{2,3},{4,5},{7}}
 => [6,3,2,5,4,1,7] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => ? = 5
{{1,4},{2,7},{3,5,6}}
 => [4,7,5,1,6,3,2] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 3
{{1,5},{2,4},{3},{6,7}}
 => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [7,5,4,3,2,1,6] => ? = 5
{{1,7},{2,4},{3,5},{6}}
 => [7,4,5,2,3,6,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 4
{{1,7},{2,4,6},{3},{5}}
 => [7,4,3,6,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 3
{{1,6},{2,5},{3,4},{7}}
 => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => ? = 6
{{1,7},{2,6},{3,4,5}}
 => [7,6,4,5,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 2
{{1,7},{2,6},{3,4},{5}}
 => [7,6,4,3,5,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 3
{{1,7},{2,6},{3,5},{4}}
 => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 0
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.