- FindStat

Identifier

Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤ

Values

([],1) => [1] => [[1]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

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

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

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

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

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

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

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

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

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

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

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

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

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

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

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

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

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

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

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

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

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

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

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

([(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 4

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

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

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

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

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

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

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

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

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

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

>>> Load all 411 entries. <<<

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

([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

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

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

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

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

([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

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

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

([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2

([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

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

([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

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

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

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

([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

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

([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2

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

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

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

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

([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2

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

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

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

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

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

([(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 4

([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

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

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

([(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 4

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

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

([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

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

([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 2

([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [[1,4,5],[2,7,8],[3,10,11],[6],[9]] => 3

([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

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

([(2,6),(3,5),(4,5),(4,6)],7) => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 4

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

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

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

([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

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

([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

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

([(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]] => 2

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

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 2

([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [[1,4,5],[2,7,8],[3,10,11],[6],[9]] => 3

([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

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

([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

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

([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 1

([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3

([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

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

([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

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

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

([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

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

([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 1

([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [[1,3,4,11],[2,6,7],[5,9,10],[8]] => 1

([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 2

([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 2

([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => [[1,3,6,7],[2,5,10,11],[4,9],[8]] => 2

([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 1

([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [[1,3,4,11],[2,6,7],[5,9,10],[8]] => 1

([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 2

([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5

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

([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

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

([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6

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

([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

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

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

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3

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

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

([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

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

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

([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,2,2,1] => [[1,3,8],[2,5,11],[4,7],[6,10],[9]] => 2

([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 3

([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 1

([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,1] => [[1,3,10,11],[2,5],[4,7],[6,9],[8]] => 1

([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [[1,3,4,11],[2,6,7],[5,9,10],[8]] => 1

([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

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

([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

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

([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

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

([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2

([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => [[1,3,6,7],[2,5,10,11],[4,9],[8]] => 2

([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [[1,3,4,11],[2,6,7],[5,9,10],[8]] => 1

([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 1

([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 2

([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2

([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2

([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

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

([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 2

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

([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 1

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

([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

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

([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

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

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

([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

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

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

([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 1

([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 1

([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2,1] => [[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]] => 1

([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2,1] => [[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]] => 2

([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 1

([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 1

([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => [[1,2,5,6,11],[3,4,9,10],[7,8]] => 1

([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 1

([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 1

([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => [[1,2,5,6,11],[3,4,9,10],[7,8]] => 1

([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 1

([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 1

([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,3,2] => [[1,2,5],[3,4,8],[6,7,11],[9,10]] => 3

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

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

([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

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

([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,3),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3,2,2] => [[1,2,7,11],[3,4,10],[5,6],[8,9]] => 1

([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 1

([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 2

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

([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

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

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

([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 2

([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 1

([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,2,2] => [[1,2,9,10,11],[3,4],[5,6],[7,8]] => 1

([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 1

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

([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 1

([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => [[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]] => 2

([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => [[1,2,5,6,11],[3,4,9,10],[7,8]] => 1

([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 1

([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 1

([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2

([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3,2] => [[1,2,5,12,13],[3,4,8],[6,7,11],[9,10]] => 1

([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2,2] => [[1,2,7,8,13],[3,4,11,12],[5,6],[9,10]] => 1

([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 1

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

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

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

([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 1

([(0,1),(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3,2] => [[1,2,5,9,14],[3,4,8,13],[6,7,12],[10,11]] => 1

([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2

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

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Description

The row containing the largest entry of a standard tableau.

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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.

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clique sizes

Description

The integer partition of the sizes of the maximal cliques of a graph.