Identifier
Values
([],1) => [2] => [1,1] => [[1],[2]] => 1
([],2) => [2,2] => [2,2] => [[1,2],[3,4]] => 1
([(0,1)],2) => [3] => [1,1,1] => [[1],[2],[3]] => 1
([],3) => [2,2,2,2] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 1
([(1,2)],3) => [6] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
([(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]] => 1
([(0,2),(1,2)],3) => [3,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
([(0,2),(0,3),(3,1)],4) => [7] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [4,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
([(1,2),(2,3)],4) => [4,4] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 1
([(0,3),(3,1),(3,2)],4) => [4,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
([(0,3),(1,3),(3,2)],4) => [4,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 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]] => 1
([(0,3),(1,2),(2,3)],4) => [7] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
([(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]] => 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]] => 3
([(0,4),(1,4),(4,2),(4,3)],5) => [4,2,2] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
([(0,4),(1,4),(2,3),(4,2)],5) => [5,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
([(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]] => 3
([(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]] => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [5,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
([(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]] => 1
([(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]] => 1
([(0,4),(2,3),(3,1),(4,2)],5) => [6] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
([(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]] => 4
([(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]] => 5
([(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]] => 5
([(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]] => 5
([(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]] => 5
([(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]] => 1
([(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]] => 5
([(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]] => 1
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
Description
The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau.
A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
This statistic equals $\max_C\big(\ell(C) - \ell(T)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
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.
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
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.