- FindStat

Identifier

Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 146 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q^{2}$

$F_{2} = q^{2} + q^{3}$

$F_{3} = 3\ q^{2} + q^{4} + q^{6}$

Description

The row containing the largest entry of a standard tableau.

Map

rowmotion cycle type

Description

The cycle type of rowmotion on the order ideals of a poset.

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

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.