- FindStat

Identifier

Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000744: Standard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [8] => [[1,2,3,4,5,6,7,8]] => 7

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

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

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

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

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

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

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

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

>>> Load all 514 entries. <<<

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

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

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

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

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

([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

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

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

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

([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

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

([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

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

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

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

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

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

([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

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

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

([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

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

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

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

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

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

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

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

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

([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3

([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

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

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

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

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

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

([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

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

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

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

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

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

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3

([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

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

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

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

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

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

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

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

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

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

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

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

([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

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

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

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

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

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

([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4

([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3

([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

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

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

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

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

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

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

([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

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

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

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

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

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

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

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

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

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

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

([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3

([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

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

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

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

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

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

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

([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [8] => [[1,2,3,4,5,6,7,8]] => 7

([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7) => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 3

([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => [[1,3,4,5,6,7,8],[2]] => 6

([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,2),(1,4),(1,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 6

([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 7

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

([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 5

([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3

([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => [[1,2,3,7,8],[4,5,6]] => 4

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 4

([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [9] => [[1,2,3,4,5,6,7,8,9]] => 8

([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 5

search for individual values

searching the database for the individual values of this statistic

Description

The length of the path to the largest entry in a standard Young tableau.

Map

to edge-partition of biconnected components

Description

Sends a graph to the partition recording the number of edges in its biconnected components.
The biconnected components are also known as blocks of a graph.

Map

reading tableau

Description

Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.