Identifier
-
Mp00060:
Permutations
—Robinson-Schensted tableau shape⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000151: Posets ⟶ ℤ
Values
[1] => [1] => [[1],[]] => ([],1) => 2
[1,2] => [2] => [[2],[]] => ([(0,1)],2) => 3
[2,1] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 3
[1,2,3] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 4
[1,3,2] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[2,1,3] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[2,3,1] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[3,1,2] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 5
[3,2,1] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 4
[1,2,3,4] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[1,2,4,3] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[1,3,2,4] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[1,3,4,2] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[1,4,2,3] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[1,4,3,2] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[2,1,3,4] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[2,1,4,3] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[2,3,1,4] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[2,3,4,1] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[2,4,1,3] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[2,4,3,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[3,1,2,4] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[3,1,4,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[3,2,1,4] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[3,2,4,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[3,4,1,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[3,4,2,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,1,2,3] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,1,3,2] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,2,1,3] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,2,3,1] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,3,1,2] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 6
[4,3,2,1] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 5
[1,2,3,4,5] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[1,2,3,5,4] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,2,4,3,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,2,4,5,3] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,2,5,3,4] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,2,5,4,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,3,2,4,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,3,2,5,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[1,3,4,2,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,3,4,5,2] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,3,5,2,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[1,3,5,4,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,4,2,3,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,4,2,5,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[1,4,3,2,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,4,3,5,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,4,5,2,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[1,4,5,3,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,5,2,3,4] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[1,5,2,4,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,5,3,2,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,5,3,4,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,5,4,2,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[1,5,4,3,2] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[2,1,3,4,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[2,1,3,5,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,1,4,3,5] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,1,4,5,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,1,5,3,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,1,5,4,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,3,1,4,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[2,3,1,5,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,3,4,1,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[2,3,4,5,1] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[2,3,5,1,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,3,5,4,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,4,1,3,5] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,4,1,5,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,4,3,1,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,4,3,5,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,4,5,1,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,4,5,3,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,5,1,3,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,5,1,4,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,5,3,1,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,5,3,4,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[2,5,4,1,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[2,5,4,3,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[3,1,2,4,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[3,1,2,5,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,1,4,2,5] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,1,4,5,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,1,5,2,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,1,5,4,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,2,1,4,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,2,1,5,4] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,2,4,1,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,2,4,5,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,2,5,1,4] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,2,5,4,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,4,1,2,5] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,4,1,5,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,4,2,1,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,4,2,5,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,4,5,1,2] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,4,5,2,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[3,5,1,2,4] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,5,1,4,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
>>> Load all 873 entries. <<<[3,5,2,1,4] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,5,2,4,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,5,4,1,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[3,5,4,2,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[4,1,2,3,5] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[4,1,2,5,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,1,3,2,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,1,3,5,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,1,5,2,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,1,5,3,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,2,1,3,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,2,1,5,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,2,3,1,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,2,3,5,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,2,5,1,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,2,5,3,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,3,1,2,5] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[4,3,1,5,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,3,2,1,5] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[4,3,2,5,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[4,3,5,1,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,3,5,2,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[4,5,1,2,3] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,5,1,3,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,5,2,1,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,5,2,3,1] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,5,3,1,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[4,5,3,2,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,1,2,3,4] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,1,2,4,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,1,3,2,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,1,3,4,2] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,1,4,2,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,1,4,3,2] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,2,1,3,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,2,1,4,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[5,2,3,1,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,2,3,4,1] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,2,4,1,3] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[5,2,4,3,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,3,1,2,4] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,3,1,4,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[5,3,2,1,4] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,3,2,4,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,3,4,1,2] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 8
[5,3,4,2,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,4,1,2,3] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 7
[5,4,1,3,2] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,4,2,1,3] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,4,2,3,1] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,4,3,1,2] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 7
[5,4,3,2,1] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[1,2,3,4,5,6] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[1,2,3,4,6,5] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,3,5,4,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,3,5,6,4] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,3,6,4,5] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,3,6,5,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,4,3,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,4,3,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,2,4,5,3,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,4,5,6,3] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,4,6,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,2,4,6,5,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,5,3,4,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,5,3,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,2,5,4,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,5,4,6,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,5,6,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,2,5,6,4,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,6,3,4,5] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,2,6,3,5,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,6,4,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,6,4,5,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,6,5,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,2,6,5,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,2,4,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,3,2,4,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,2,5,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,2,5,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,2,6,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,2,6,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,3,4,2,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,3,4,2,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,4,5,2,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,3,4,5,6,2] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,3,4,6,2,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,4,6,5,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,5,2,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,5,2,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,5,4,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,5,4,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,5,6,2,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,5,6,4,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,6,2,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,3,6,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,3,6,4,2,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,6,4,5,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,3,6,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,3,6,5,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,2,3,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,4,2,3,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,2,5,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,2,5,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,2,6,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,2,6,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,3,2,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,3,2,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,3,5,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,3,5,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,3,6,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,3,6,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,5,2,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,5,2,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,5,3,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,5,3,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,5,6,2,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,5,6,3,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,4,6,2,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,4,6,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,6,3,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,6,3,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,6,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,4,6,5,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,2,3,4,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,5,2,3,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,5,2,4,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,2,4,6,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,2,6,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,5,2,6,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,3,2,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,3,2,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,3,4,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,3,4,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,3,6,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,3,6,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,4,2,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,4,2,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,4,3,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,4,3,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,4,6,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,4,6,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,5,6,2,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[1,5,6,2,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,6,3,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,6,3,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,6,4,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,5,6,4,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,2,3,4,5] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[1,6,2,3,5,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,2,4,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,2,4,5,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,2,5,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,2,5,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,3,2,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,3,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,6,3,4,2,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,3,4,5,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,3,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,6,3,5,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,4,2,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,4,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,6,4,3,2,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,4,3,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,4,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[1,6,4,5,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,2,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,2,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,3,2,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,3,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,4,2,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[1,6,5,4,3,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,1,3,4,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,1,3,4,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,3,5,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,3,5,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,3,6,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,3,6,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,4,3,5,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,4,3,6,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,1,4,5,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,4,5,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,4,6,3,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,1,4,6,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,5,3,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,5,3,6,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,1,5,4,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,5,4,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,5,6,3,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,1,5,6,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,6,3,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,1,6,3,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,6,4,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,6,4,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,6,5,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,1,6,5,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,1,4,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,3,1,4,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,1,5,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,1,5,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,1,6,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,1,6,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,3,4,1,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,3,4,1,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,4,5,1,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,3,4,5,6,1] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[2,3,4,6,1,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,4,6,5,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,5,1,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,5,1,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,5,4,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,5,4,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,5,6,1,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,5,6,4,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,6,1,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,3,6,1,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,3,6,4,1,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,6,4,5,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,3,6,5,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,3,6,5,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,1,3,5,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,1,3,6,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,4,1,5,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,1,5,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,1,6,3,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,4,1,6,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,3,1,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,3,1,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,3,5,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,3,5,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,3,6,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,3,6,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,5,1,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,5,1,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,5,3,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,5,3,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,5,6,1,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,4,5,6,3,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,4,6,1,3,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,4,6,1,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,6,3,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,6,3,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,6,5,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,4,6,5,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,1,3,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,5,1,3,6,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,5,1,4,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,1,4,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,1,6,3,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,5,1,6,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,3,1,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,3,1,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,3,4,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,3,4,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,3,6,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,3,6,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,4,1,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,4,1,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,4,3,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,4,3,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,4,6,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,4,6,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,5,6,1,3,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[2,5,6,1,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,6,3,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,6,3,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,6,4,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,5,6,4,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,1,3,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,6,1,3,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,1,4,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,1,4,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,1,5,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,1,5,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,6,3,1,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,3,1,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,3,4,1,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,3,4,5,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,3,5,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,3,5,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,4,1,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,4,1,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,4,3,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,4,3,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,4,5,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,4,5,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,5,1,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[2,6,5,1,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,6,5,3,1,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,5,3,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[2,6,5,4,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[2,6,5,4,3,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[3,1,2,4,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[3,1,2,4,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,2,5,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,2,5,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,2,6,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,2,6,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,4,2,5,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,4,2,6,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,1,4,5,2,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,4,5,6,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,4,6,2,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,1,4,6,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,5,2,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,5,2,6,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,1,5,4,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,5,4,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,5,6,2,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,1,5,6,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,6,2,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,1,6,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,6,4,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,6,4,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,6,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,1,6,5,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,2,1,4,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,2,1,4,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,1,5,4,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,1,5,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,1,6,4,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,1,6,5,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,2,4,1,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,2,4,1,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,4,5,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,2,4,5,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,2,4,6,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,4,6,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,1,4,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,1,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,4,1,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,4,6,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,6,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,5,6,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,6,1,4,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,6,1,5,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,2,6,4,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,6,4,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,2,6,5,1,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,2,6,5,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,1,2,5,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,1,2,6,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,4,1,5,2,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,1,5,6,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,1,6,2,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,4,1,6,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,2,1,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,2,1,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,2,5,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,2,5,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,2,6,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,2,6,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,5,1,2,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,5,1,6,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,5,2,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,5,2,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,5,6,1,2] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,4,5,6,2,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,4,6,1,2,5] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,4,6,1,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,6,2,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,6,2,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,6,5,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,4,6,5,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,5,1,2,4,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,5,1,2,6,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,5,1,4,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,1,4,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,1,6,2,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,5,1,6,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,1,4,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,1,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,4,1,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,4,6,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,6,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,2,6,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,4,1,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,4,1,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,4,2,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,5,4,2,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,5,4,6,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,4,6,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,5,6,1,2,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,5,6,1,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,6,2,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,6,2,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,6,4,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,5,6,4,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,6,1,2,4,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,1,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,1,4,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,1,4,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,1,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,1,5,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,2,1,4,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,2,1,5,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,6,2,4,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,2,4,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,2,5,1,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[3,6,2,5,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,4,1,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,4,1,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,4,2,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,6,4,2,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,6,4,5,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,4,5,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[3,6,5,1,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[3,6,5,1,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,5,2,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,5,2,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,5,4,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[3,6,5,4,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[4,1,2,3,5,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[4,1,2,3,6,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,2,5,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,2,5,6,3] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,2,6,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,2,6,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,3,2,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,1,3,2,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,3,5,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,1,3,5,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,1,3,6,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,3,6,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,5,2,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,5,2,6,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,1,5,3,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,5,3,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,5,6,2,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,1,5,6,3,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,6,2,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,1,6,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,6,3,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,6,3,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,6,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,1,6,5,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,2,1,3,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,2,1,3,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,1,5,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,1,5,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,1,6,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,1,6,5,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,2,3,1,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,2,3,1,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,3,5,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,2,3,5,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,2,3,6,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,3,6,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,1,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,1,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,3,1,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,3,6,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,6,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,5,6,3,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,6,1,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,6,1,5,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,2,6,3,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,6,3,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,2,6,5,1,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,2,6,5,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,1,2,5,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,1,2,6,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,1,5,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,1,5,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,1,6,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,1,6,5,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,3,2,1,5,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,2,1,6,5] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,2,5,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,2,5,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,2,6,1,5] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,2,6,5,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,5,1,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,5,1,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,5,2,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,5,2,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,5,6,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,5,6,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,3,6,1,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,3,6,1,5,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,3,6,2,1,5] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,6,2,5,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,3,6,5,1,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,3,6,5,2,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,5,1,2,3,6] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,5,1,2,6,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,5,1,3,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,1,3,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,1,6,2,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,5,1,6,3,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,1,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,1,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,3,1,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,3,6,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,6,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,2,6,3,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,3,1,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,3,1,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,3,2,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,5,3,2,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,5,3,6,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,3,6,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,5,6,1,2,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,5,6,1,3,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,6,2,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,6,2,3,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,6,3,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,5,6,3,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[4,6,1,2,3,5] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,1,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,1,3,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,1,3,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,1,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,1,5,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,2,1,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,2,1,5,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,6,2,3,1,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,2,3,5,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,2,5,1,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,6,2,5,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,3,1,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,3,1,5,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,6,3,2,1,5] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,3,2,5,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,3,5,1,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[4,6,3,5,2,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,5,1,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[4,6,5,1,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,5,2,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,5,2,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,5,3,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[4,6,5,3,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,1,2,3,4,6] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,1,2,3,6,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,1,2,4,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,2,4,6,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,2,6,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,1,2,6,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,3,2,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,3,2,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,3,4,2,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,3,4,6,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,3,6,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,3,6,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,4,2,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,4,2,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,4,3,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,4,3,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,4,6,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,4,6,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,1,6,2,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,1,6,2,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,6,3,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,6,3,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,6,4,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,1,6,4,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,2,1,3,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,1,3,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,1,4,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,1,4,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,1,6,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,1,6,4,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,2,3,1,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,3,1,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,3,4,1,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,3,4,6,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,3,6,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,3,6,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,4,1,3,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,4,1,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,4,3,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,4,3,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,4,6,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,4,6,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,2,6,1,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,6,1,4,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,2,6,3,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,6,3,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,2,6,4,1,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,2,6,4,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,1,2,4,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,1,2,6,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,1,4,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,1,4,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,1,6,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,1,6,4,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,3,2,1,4,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,2,1,6,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,2,4,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,2,4,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,2,6,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,2,6,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,4,1,2,6] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,4,1,6,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,4,2,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,4,2,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,4,6,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,4,6,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,3,6,1,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,3,6,1,4,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,3,6,2,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,6,2,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,3,6,4,1,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,3,6,4,2,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,1,2,3,6] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,1,2,6,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,4,1,3,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,1,3,6,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,1,6,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,4,1,6,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,2,1,3,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,2,1,6,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,2,3,1,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,2,3,6,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,2,6,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,2,6,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,3,1,2,6] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[5,4,3,1,6,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,3,2,1,6] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,4,3,2,6,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,4,3,6,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,3,6,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,4,6,1,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,4,6,1,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,6,2,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,6,2,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,6,3,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,4,6,3,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[5,6,1,2,3,4] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,1,2,4,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,1,3,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,1,3,4,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,1,4,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,1,4,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,2,1,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,2,1,4,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,6,2,3,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,2,3,4,1] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,2,4,1,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,6,2,4,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,3,1,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,3,1,4,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,6,3,2,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,3,2,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,3,4,1,2] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 9
[5,6,3,4,2,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,4,1,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[5,6,4,1,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,4,2,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,4,2,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,4,3,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[5,6,4,3,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,1,2,3,4,5] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,1,2,3,5,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,2,4,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,2,4,5,3] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,2,5,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,2,5,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,3,2,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,3,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,1,3,4,2,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,3,4,5,2] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,3,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,1,3,5,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,4,2,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,4,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,1,4,3,2,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,4,3,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,4,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,1,4,5,3,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,2,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,2,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,3,2,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,3,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,4,2,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,1,5,4,3,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,2,1,3,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,1,3,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,1,4,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,1,4,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,1,5,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,1,5,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,2,3,1,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,3,1,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,3,4,1,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,3,4,5,1] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,3,5,1,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,3,5,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,4,1,3,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,4,1,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,4,3,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,4,3,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,4,5,1,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,4,5,3,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,5,1,3,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,2,5,1,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,2,5,3,1,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,5,3,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,2,5,4,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,2,5,4,3,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,3,1,2,4,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,1,2,5,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,1,4,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,1,4,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,1,5,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,1,5,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,2,1,4,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,2,1,5,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,2,4,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,2,4,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,2,5,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,2,5,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,4,1,2,5] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,4,1,5,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,4,2,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,4,2,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,4,5,1,2] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,4,5,2,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,3,5,1,2,4] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,3,5,1,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,5,2,1,4] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,5,2,4,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,5,4,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,3,5,4,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,4,1,2,3,5] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,1,2,5,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,4,1,3,2,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,1,3,5,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,1,5,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,4,1,5,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,2,1,3,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,2,1,5,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,2,3,1,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,2,3,5,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,2,5,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,2,5,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,3,1,2,5] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,4,3,1,5,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,3,2,1,5] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,4,3,2,5,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,4,3,5,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,3,5,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,4,5,1,2,3] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 10
[6,4,5,1,3,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,5,2,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,5,2,3,1] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,5,3,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,4,5,3,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,1,2,3,4] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,1,2,4,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,1,3,2,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,1,3,4,2] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,1,4,2,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,1,4,3,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,2,1,3,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,2,1,4,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,5,2,3,1,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,2,3,4,1] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,2,4,1,3] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,5,2,4,3,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,3,1,2,4] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,3,1,4,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,5,3,2,1,4] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,3,2,4,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,3,4,1,2] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 9
[6,5,3,4,2,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,4,1,2,3] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 8
[6,5,4,1,3,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,4,2,1,3] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,4,2,3,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,4,3,1,2] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 8
[6,5,4,3,2,1] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,4 2,22 2,68,50 2,250,212,256
F1=q2
F2=2 q3
F3=2 q4+4 q5
F4=2 q5+22 q6
F5=2 q6+68 q7+50 q8
F6=2 q7+250 q8+212 q9+256 q10
Description
The number of facets in the chain polytope of the poset.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell d is greater than a cell c if the entry in d must be larger than the entry of c in any standard Young tableau on the skew partition.
This is the poset on the cells of the Young diagram, such that a cell d is greater than a cell c if the entry in d must be larger than the entry of c in any standard Young tableau on the skew partition.
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