- FindStat

Identifier

Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 218 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5,5,5] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)

[5,4,3,2,1] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => ([(0,7),(0,8),(3,5),(3,12),(4,6),(4,13),(5,2),(5,10),(6,1),(6,11),(7,3),(7,9),(8,4),(8,9),(9,12),(9,13),(12,10),(12,14),(13,11),(13,14)],15)

[4,4,4,3] => [4,4,4,3] => [[4,4,4,3],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,3),(2,13),(3,9),(4,10),(5,2),(5,11),(6,1),(6,11),(9,7),(10,8),(11,13),(11,14),(12,7),(12,8),(13,9),(13,12),(14,10),(14,12)],15)

[4,3,3,3,2] => [5,5,4,1] => [[5,5,4,1],[]] => ([(0,6),(0,7),(2,9),(3,2),(3,11),(4,3),(4,12),(5,1),(5,10),(6,4),(6,8),(7,5),(7,8),(8,10),(8,12),(10,13),(11,9),(11,14),(12,11),(12,13),(13,14)],15)

[3,3,3,3,3] => [5,5,5] => [[5,5,5],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)

[6,5,5] => [3,3,3,3,3,1] => [[3,3,3,3,3,1],[]] => ([(0,6),(0,7),(2,12),(3,4),(3,15),(4,5),(4,13),(5,1),(5,11),(6,2),(6,14),(7,3),(7,14),(9,10),(10,8),(11,8),(12,9),(13,10),(13,11),(14,12),(14,15),(15,9),(15,13)],16)

[5,4,4,3] => [4,4,4,3,1] => [[4,4,4,3,1],[]] => ([(0,6),(0,7),(2,5),(2,14),(3,4),(3,15),(4,11),(5,1),(5,10),(6,2),(6,12),(7,3),(7,12),(10,8),(11,9),(12,14),(12,15),(13,8),(13,9),(14,10),(14,13),(15,11),(15,13)],16)

[4,4,4,4] => [4,4,4,4] => [[4,4,4,4],[]] => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)

[4,3,3,3,3] => [5,5,5,1] => [[5,5,5,1],[]] => ([(0,6),(0,7),(2,5),(2,15),(3,1),(3,12),(4,11),(5,4),(5,13),(6,2),(6,14),(7,3),(7,14),(9,10),(10,8),(11,8),(12,9),(13,10),(13,11),(14,12),(14,15),(15,9),(15,13)],16)

[5,4,4,4] => [4,4,4,4,1] => [[4,4,4,4,1],[]] => ([(0,6),(0,7),(2,5),(2,15),(3,4),(3,16),(4,10),(5,1),(5,9),(6,2),(6,14),(7,3),(7,14),(9,11),(10,12),(11,8),(12,8),(13,11),(13,12),(14,15),(14,16),(15,9),(15,13),(16,10),(16,13)],17)

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

[6,5,5,5] => [4,4,4,4,4,1] => [[4,4,4,4,4,1],[]] => ([(0,7),(0,8),(2,4),(2,17),(3,6),(3,16),(4,13),(5,1),(5,14),(6,5),(6,20),(7,2),(7,18),(8,3),(8,18),(10,12),(11,9),(12,9),(13,10),(14,11),(15,10),(15,19),(16,15),(16,20),(17,13),(17,15),(18,16),(18,17),(19,11),(19,12),(20,14),(20,19)],21)

[5,4,4,4,4] => [5,5,5,5,1] => [[5,5,5,5,1],[]] => ([(0,7),(0,8),(2,5),(2,17),(3,6),(3,16),(4,14),(5,1),(5,13),(6,4),(6,20),(7,2),(7,18),(8,3),(8,18),(10,12),(11,9),(12,9),(13,10),(14,11),(15,10),(15,19),(16,15),(16,20),(17,13),(17,15),(18,16),(18,17),(19,11),(19,12),(20,14),(20,19)],21)

Map

conjugate

Description

Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.

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.