Identifier
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Images
[1] => [[1],[]] => ([],1)
[2] => [[2],[]] => ([(0,1)],2)
[1,1] => [[1,1],[]] => ([(0,1)],2)
[3] => [[3],[]] => ([(0,2),(2,1)],3)
[2,1] => [[2,1],[]] => ([(0,1),(0,2)],3)
[1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3)
[4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4)
[3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4)
[2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4)
[1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4)
[5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5)
[3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
[3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5)
[2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
[2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5)
[1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
[4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
[3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
[3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
[2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
[2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[6,1] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[5,2] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)
[5,1,1] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
[4,3] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
[4,2,1] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
[4,1,1,1] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
[3,3,1] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
[3,2,2] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
[3,2,1,1] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
[3,1,1,1,1] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
[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)
[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)
[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)
[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)
[8] => [[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[7,1] => [[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[6,2] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8)
[6,1,1] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
[5,3] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8)
[5,2,1] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8)
[5,1,1,1] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
[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)
[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)
[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)
[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] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
[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] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[9] => [[9],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[8,1] => [[8,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
[7,2] => [[7,2],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9)
[7,1,1] => [[7,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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] => [[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)
[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)
[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)
[4,2,2,1] => [[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)
[4,2,1,1,1] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9)
[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)
[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] => [[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[10] => [[10],[]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[9,1] => [[9,1],[]] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[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)
[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)
[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)
>>> Load all 218 entries. <<<
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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] => [[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)
[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)
[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)
[4,3,3] => [[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)
[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] => [[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)
[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)
[4,2,2,1,1] => [[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[4,4,1,1,1] => [[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)
[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] => [[4,3,2,2],[]] => ([(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)
[4,3,2,1,1] => [[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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] => [[5,2,2,2,1],[]] => ([(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)
[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)
[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)
[4,4,2,2] => [[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] => [[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)
[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)
[4,3,3,1,1] => [[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[5,4,4] => [[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)
[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)
[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)
[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)
[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)
[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] => [[5,3,2,2,1],[]] => ([(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)
[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)
[4,4,3,2] => [[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] => [[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)
[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)
[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)
[4,3,3,2,1] => [[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)
[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)
[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)
[5,5,4] => [[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)
[5,4,3,2] => [[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)
[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)
[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] => [[5,3,3,2,1],[]] => ([(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)
[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)
[4,4,3,3] => [[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)
[4,4,3,2,1] => [[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)
[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)
[5,5,5] => [[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)
[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)
[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],[]] => ([(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)
[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)
[5,5,5,1] => [[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)
[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)
[4,4,4,3,1] => [[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)
[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)
[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)
[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)
[5,5,5,5,1] => [[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
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.