- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001060: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 469 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).

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.

Map

major-index to inversion-number bijection

Description

Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.