- FindStat

Identifier

Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000673: Permutations ⟶ ℤ

Values

[1,0,1,0] => [2,1] => {{1,2}} => [2,1] => 2

[1,1,0,0] => [1,2] => {{1},{2}} => [1,2] => 0

[1,0,1,0,1,0] => [2,3,1] => {{1,2,3}} => [2,3,1] => 3

[1,0,1,1,0,0] => [2,1,3] => {{1,2},{3}} => [2,1,3] => 2

[1,1,0,0,1,0] => [1,3,2] => {{1},{2,3}} => [1,3,2] => 2

[1,1,0,1,0,0] => [3,1,2] => {{1,3},{2}} => [3,2,1] => 2

[1,1,1,0,0,0] => [1,2,3] => {{1},{2},{3}} => [1,2,3] => 0

[1,0,1,0,1,0,1,0] => [2,3,4,1] => {{1,2,3,4}} => [2,3,4,1] => 4

[1,0,1,0,1,1,0,0] => [2,3,1,4] => {{1,2,3},{4}} => [2,3,1,4] => 3

[1,0,1,1,0,0,1,0] => [2,1,4,3] => {{1,2},{3,4}} => [2,1,4,3] => 4

[1,0,1,1,0,1,0,0] => [2,4,1,3] => {{1,2,4},{3}} => [2,4,3,1] => 3

[1,0,1,1,1,0,0,0] => [2,1,3,4] => {{1,2},{3},{4}} => [2,1,3,4] => 2

[1,1,0,0,1,0,1,0] => [1,3,4,2] => {{1},{2,3,4}} => [1,3,4,2] => 3

[1,1,0,0,1,1,0,0] => [1,3,2,4] => {{1},{2,3},{4}} => [1,3,2,4] => 2

[1,1,0,1,0,0,1,0] => [3,1,4,2] => {{1,3,4},{2}} => [3,2,4,1] => 3

[1,1,0,1,0,1,0,0] => [3,4,1,2] => {{1,3},{2,4}} => [3,4,1,2] => 4

[1,1,0,1,1,0,0,0] => [3,1,2,4] => {{1,3},{2},{4}} => [3,2,1,4] => 2

[1,1,1,0,0,0,1,0] => [1,2,4,3] => {{1},{2},{3,4}} => [1,2,4,3] => 2

[1,1,1,0,0,1,0,0] => [1,4,2,3] => {{1},{2,4},{3}} => [1,4,3,2] => 2

[1,1,1,0,1,0,0,0] => [4,1,2,3] => {{1,4},{2},{3}} => [4,2,3,1] => 2

[1,1,1,1,0,0,0,0] => [1,2,3,4] => {{1},{2},{3},{4}} => [1,2,3,4] => 0

[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 5

[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 4

[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 5

[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => {{1,2,3,5},{4}} => [2,3,5,4,1] => 4

[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 3

[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 5

[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 4

[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => {{1,2,4,5},{3}} => [2,4,3,5,1] => 4

[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 5

[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => {{1,2,4},{3},{5}} => [2,4,3,1,5] => 3

[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 4

[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => {{1,2},{3,5},{4}} => [2,1,5,4,3] => 4

[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 3

[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 2

[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 4

[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 3

[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 4

[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => {{1},{2,3,5},{4}} => [1,3,5,4,2] => 3

[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 2

[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 4

[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => {{1,3,4},{2},{5}} => [3,2,4,1,5] => 3

[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 5

[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => {{1,3,5},{2,4}} => [3,4,5,2,1] => 5

[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 4

[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => {{1,3},{2},{4,5}} => [3,2,1,5,4] => 4

[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 3

[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 4

[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => 2

[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 3

[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 2

[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => {{1},{2,4,5},{3}} => [1,4,3,5,2] => 3

[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 4

[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => 2

[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 3

[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 4

[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 4

[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 2

[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 2

[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => 2

[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 2

[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 2

[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0

[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 6

[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 5

[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 6

[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 5

[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 4

[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 6

[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 5

[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 5

[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 6

[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 4

[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 5

[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 5

[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 4

[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 3

[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 6

[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 5

[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 6

[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => 5

[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 4

[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 5

[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 4

[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 6

[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 6

[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 5

[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 5

[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 4

[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 5

[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 3

[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 5

[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 4

[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => 5

[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 6

[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => 4

[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 4

[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 5

[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 5

[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 3

[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 4

>>> Load all 305 entries. <<<

[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => 4

[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 4

[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 3

[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 2

[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 5

[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 4

[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 5

[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => 4

[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 3

[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 5

[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 4

[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 4

[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 5

[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => 3

[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 4

[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => 4

[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 3

[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 2

[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 5

[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => 4

[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => 5

[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 4

[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => 3

[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 6

[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 5

[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => 6

[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 6

[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => 5

[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 6

[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 5

[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 5

[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 4

[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => 5

[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => 4

[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 4

[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 5

[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 3

[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 5

[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 6

[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 5

[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 4

[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => 4

[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 4

[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 3

[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 4

[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => 2

[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 4

[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 3

[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 4

[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => 3

[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 2

[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => 4

[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => 3

[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 5

[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => 5

[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 4

[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => 4

[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 3

[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 4

[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => 2

[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 4

[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 3

[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 5

[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 5

[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 4

[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 5

[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 5

[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 6

[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 4

[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 4

[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 3

[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 4

[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 4

[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 2

[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 3

[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 2

[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => 3

[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 4

[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => 2

[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 3

[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 4

[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 4

[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 2

[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 3

[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 4

[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 4

[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 4

[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 2

[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 2

[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => 2

[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 2

[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 2

[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 2

[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 6

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 5

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 6

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => {{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => 5

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 4

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 6

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 5

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => 5

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 6

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => {{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => 4

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 5

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => {{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => 5

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => {{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => 4

[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 3

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 6

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 5

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => 6

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => {{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => 5

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => 4

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => 5

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => {{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => 4

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 6

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => {{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => 6

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 5

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => {{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => 5

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => {{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => 4

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => {{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => 5

[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => {{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => 3

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 5

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => 4

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => {{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => 5

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => 6

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => 4

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => {{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => 4

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => {{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => 5

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => {{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => 5

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => {{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => 3

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => 4

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => 4

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => 4

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => {{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => 3

[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => 2

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 5

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 4

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 5

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => {{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => 4

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 3

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 5

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => 4

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => {{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => 4

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 5

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => {{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => 3

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => 4

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => 4

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => 3

[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => 2

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => {{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => 5

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => {{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => 4

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => {{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => 5

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => {{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => 4

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => {{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => 3

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 6

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 5

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => {{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => 6

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 6

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => {{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => 5

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => 6

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => {{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => 5

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => {{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => 5

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => 4

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => {{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => 5

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => 4

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => {{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => 4

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => {{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => 5

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => {{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => 3

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => {{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => 5

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => 6

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => 4

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => 4

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => {{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => 4

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => {{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => 3

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => 2

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 4

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 3

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => 4

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => 3

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => 2

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => {{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => 4

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => {{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => 3

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 5

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => {{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => 5

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => 4

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => 4

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => {{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => 3

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => 4

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => 2

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 3

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => 2

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => {{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => 3

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => 4

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => 2

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => {{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => 3

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => {{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => 4

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => {{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => 4

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => 2

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => 2

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => 2

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => 2

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => 0

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$F_{2} = 1 + q^{2}$

$F_{3} = 1 + 3\ q^{2} + q^{3}$

$F_{4} = 1 + 6\ q^{2} + 4\ q^{3} + 3\ q^{4}$

$F_{5} = 1 + 10\ q^{2} + 10\ q^{3} + 15\ q^{4} + 6\ q^{5}$

$F_{6} = 1 + 15\ q^{2} + 20\ q^{3} + 45\ q^{4} + 36\ q^{5} + 15\ q^{6}$

Description

The number of non-fixed points of a permutation.
In other words, this statistic is

$n$ minus the number of fixed points (St000022The number of fixed points of a permutation.) of

$\pi$ .

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs

$(i, \pi(i))$ with

$i\leq\pi(i)$ .