- FindStat

Identifier

Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤ

Values

[3,2,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3) => 3

[4,2,3,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4

[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4

[5,2,3,4,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4

[5,2,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4

[5,3,2,4,1] => [5,3,2,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4

[5,3,4,2,1] => [5,3,4,2,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 5

[5,4,2,3,1] => [5,4,2,3,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 5

[5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[6,2,3,4,5,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,2,3,5,4,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,2,4,3,5,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,2,4,5,3,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,2,5,3,4,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,2,5,4,3,1] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,3,2,4,5,1] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 4

[6,3,2,5,4,1] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 4

[6,3,4,2,5,1] => [6,3,5,2,4,1] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6

[6,3,4,5,2,1] => [6,3,5,4,2,1] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5

[6,3,5,2,4,1] => [6,3,5,2,4,1] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6

[6,3,5,4,2,1] => [6,3,5,4,2,1] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5

[6,4,2,3,5,1] => [6,4,2,5,3,1] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6

[6,4,2,5,3,1] => [6,4,2,5,3,1] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6

[6,4,3,2,5,1] => [6,4,3,2,5,1] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 4

[6,4,3,5,2,1] => [6,4,3,5,2,1] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5

[6,4,5,3,2,1] => [6,4,5,3,2,1] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 6

[6,5,2,3,4,1] => [6,5,2,4,3,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5

[6,5,2,4,3,1] => [6,5,2,4,3,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5

[6,5,3,2,4,1] => [6,5,3,2,4,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5

[6,5,3,4,2,1] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6

[6,5,4,2,3,1] => [6,5,4,2,3,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6

[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[7,2,3,4,5,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,3,4,6,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,3,5,4,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,3,5,6,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,3,6,4,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,3,6,5,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,3,5,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,3,6,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,5,3,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,5,6,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,6,3,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,4,6,5,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,3,4,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,3,6,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,4,3,6,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,4,6,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,6,3,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,5,6,4,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,3,4,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,3,5,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,4,3,5,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,4,5,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,5,3,4,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,2,6,5,4,3,1] => [7,2,6,5,4,3,1] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 4

[7,3,2,4,5,6,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,2,4,6,5,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,2,5,4,6,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,2,5,6,4,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,2,6,4,5,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,2,6,5,4,1] => [7,3,2,6,5,4,1] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,3,4,2,5,6,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,4,2,6,5,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,4,5,2,6,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,4,5,6,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,3,4,6,2,5,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,4,6,5,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,3,5,2,4,6,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,5,2,6,4,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,5,4,2,6,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,5,4,6,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,3,5,6,2,4,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,5,6,4,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,3,6,2,4,5,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,6,2,5,4,1] => [7,3,6,2,5,4,1] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,3,6,4,2,5,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,6,4,5,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,3,6,5,2,4,1] => [7,3,6,5,2,4,1] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,3,6,5,4,2,1] => [7,3,6,5,4,2,1] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 5

[7,4,2,3,5,6,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,2,3,6,5,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,2,5,3,6,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,2,5,6,3,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,2,6,3,5,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,2,6,5,3,1] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,3,2,5,6,1] => [7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,4,3,2,6,5,1] => [7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 4

[7,4,3,5,2,6,1] => [7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,3,5,6,2,1] => [7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 5

[7,4,3,6,2,5,1] => [7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 6

[7,4,3,6,5,2,1] => [7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 5

[7,4,5,3,2,6,1] => [7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,4,5,3,6,2,1] => [7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 7

[7,4,5,6,3,2,1] => [7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 6

[7,4,6,3,2,5,1] => [7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,4,6,3,5,2,1] => [7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 7

[7,4,6,5,3,2,1] => [7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 6

[7,5,2,3,4,6,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,5,2,3,6,4,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,5,2,4,3,6,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

>>> Load all 138 entries. <<<

[7,5,2,4,6,3,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,5,2,6,3,4,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,5,2,6,4,3,1] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 6

[7,5,3,2,4,6,1] => [7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,5,3,2,6,4,1] => [7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 6

[7,5,3,4,6,2,1] => [7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 7

[7,5,3,6,4,2,1] => [7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 7

[7,5,4,2,3,6,1] => [7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,5,4,2,6,3,1] => [7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 6

[7,5,4,3,2,6,1] => [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) => 4

[7,5,4,3,6,2,1] => [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) => 5

[7,5,4,6,3,2,1] => [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) => 6

[7,5,6,4,2,3,1] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 7

[7,5,6,4,3,2,1] => [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) => 7

[7,6,2,3,4,5,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,2,3,5,4,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,2,4,3,5,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,2,4,5,3,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,2,5,3,4,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,2,5,4,3,1] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 5

[7,6,3,2,4,5,1] => [7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 5

[7,6,3,2,5,4,1] => [7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 5

[7,6,3,4,2,5,1] => [7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 7

[7,6,3,4,5,2,1] => [7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 6

[7,6,3,5,2,4,1] => [7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 7

[7,6,3,5,4,2,1] => [7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 6

[7,6,4,2,3,5,1] => [7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 7

[7,6,4,2,5,3,1] => [7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 7

[7,6,4,3,2,5,1] => [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) => 5

[7,6,4,3,5,2,1] => [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) => 6

[7,6,4,5,3,2,1] => [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) => 7

[7,6,5,2,3,4,1] => [7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 6

[7,6,5,2,4,3,1] => [7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 6

[7,6,5,3,2,4,1] => [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) => 6

[7,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 7

[7,6,5,4,2,3,1] => [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) => 7

[7,6,5,4,3,2,1] => [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) => 7

search for individual values

searching the database for the individual values of this statistic

Description

The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.

Map

complement

Description

Sents a permutation to its complement.
The complement of a permutation

$\sigma$ of length

$n$ is the permutation

$\tau$ with

$\tau(i) = n+1-\sigma(i)$

Map

Simion-Schmidt map

Description

The Simion-Schmidt map sends any permutation to a

$123$ -avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between

$132$ -avoiding permutations and

$123$ -avoiding permutations, see [1, Proposition 19].

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$
and the cover relation is given by

$(w, x) \leq (y, z)$ if

$w \leq y$ and

$x \leq z$ .
For example, the permutation

$[3,1,5,4,2]$ is mapped to the poset with cover relations

$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$