Identifier
-
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000777: Graphs ⟶ ℤ
Values
[1,0,1,0] => [3,1,2] => [3,1,2] => ([(0,2),(1,2)],3) => 3
[1,0,1,0,1,0] => [4,1,2,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 3
[1,1,0,0,1,0] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4) => 4
[1,1,0,1,0,0] => [4,3,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4) => 4
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 5
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 5
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 5
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 3
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 5
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 4
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [3,4,6,2,1,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [3,4,6,1,5,2] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 6
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [3,5,2,6,1,4] => ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [3,5,6,4,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 6
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [3,5,6,1,4,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [3,6,2,4,1,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [4,2,5,6,1,3] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 6
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [4,2,6,3,1,5] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 5
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [4,5,3,6,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 6
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [4,6,3,2,1,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [4,6,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [4,6,1,3,5,2] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [5,2,3,6,1,4] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [5,2,6,4,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,2,6,1,4,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 5
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,6,3,1,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 5
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,6,1,4,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 5
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,3,1,5,4] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,2,1,4,5,3] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,1,3,4,5,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [3,4,5,7,2,1,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [3,4,5,7,1,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7) => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [3,4,6,2,7,1,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [3,4,6,7,5,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [3,4,6,7,1,5,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [3,4,7,2,5,1,6] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [3,4,7,2,1,6,5] => ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [3,4,7,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [3,5,2,6,7,1,4] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [3,5,2,7,4,1,6] => ([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 7
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [3,5,2,7,1,6,4] => ([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7) => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [3,5,6,4,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [3,5,6,7,4,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [3,5,6,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [3,5,7,4,2,1,6] => ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [3,5,7,4,1,6,2] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [3,5,7,1,4,6,2] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [3,6,2,4,7,1,5] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [3,6,2,7,5,1,4] => ([(0,3),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [3,6,2,7,1,5,4] => ([(0,4),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [3,6,7,4,5,1,2] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [3,6,7,4,1,5,2] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [3,6,7,1,5,4,2] => ([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 7
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [3,7,2,4,5,1,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [3,7,2,4,1,6,5] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [3,7,2,1,5,6,4] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [3,7,1,4,5,6,2] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [4,2,5,6,7,1,3] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7) => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [4,2,5,7,3,1,6] => ([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [4,2,5,7,1,6,3] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [4,2,6,3,7,1,5] => ([(0,1),(0,6),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [4,2,6,7,5,1,3] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [4,2,6,7,1,5,3] => ([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [4,2,7,3,5,1,6] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [4,2,7,3,1,6,5] => ([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [4,2,7,1,5,6,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [4,5,3,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [4,5,3,7,2,1,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [4,5,3,7,1,6,2] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [4,5,6,3,7,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [4,5,6,7,2,1,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [4,5,6,7,1,3,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [4,5,7,3,2,1,6] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [4,5,7,3,1,6,2] => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [4,5,7,1,2,6,3] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [4,6,3,2,7,1,5] => ([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [4,6,3,7,5,1,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [4,6,3,7,1,5,2] => ([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [4,6,7,3,5,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 7
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [4,6,7,3,1,5,2] => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [4,6,7,1,5,2,3] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [4,7,3,2,5,1,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [4,7,3,2,1,6,5] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [4,7,3,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [4,7,1,3,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [5,2,3,6,7,1,4] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 6
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [5,2,3,7,4,1,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [5,2,3,7,1,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => 7
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [5,2,6,4,7,1,3] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 7
>>> Load all 132 entries. <<<
search for individual values
searching the database for the individual values of this statistic
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
searching the database
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!