- FindStat

Identifier

Mp00214: Semistandard tableaux —subcrystal⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000510: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 381 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The number of invariant oriented cycles when acting with a permutation of given cycle type.

Map

promotion cycle type

Description

The cycle type of promotion on the linear extensions of a poset.

Map

subcrystal

Description

The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.