- FindStat

Identifier

Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000734: Standard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 167 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$F_{4} = q^{2} + 4\ q^{3} + 4\ q^{4} + 2\ q^{5} + 3\ q^{6} + 2\ q^{7}$

Description

The last entry in the first row of a standard tableau.

Map

initial tableau

Description

Sends an integer partition to the standard tableau obtained by filling the numbers

$1$ through

$n$ row by row.

Map

rowmotion cycle type

Description

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