Identifier
Values
([(0,3),(1,2)],4) => [1,1] => [1] => 0
([(1,4),(2,3)],5) => [1,1] => [1] => 0
([(0,1),(2,4),(3,4)],5) => [2,1] => [1] => 0
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [1] => 0
([(2,5),(3,4)],6) => [1,1] => [1] => 0
([(1,2),(3,5),(4,5)],6) => [2,1] => [1] => 0
([(0,1),(2,5),(3,5),(4,5)],6) => [3,1] => [1] => 0
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2] => [2] => 0
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [1,1] => 0
([(0,1),(2,5),(3,4),(4,5)],6) => [3,1] => [1] => 0
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [1] => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,1] => [1] => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [1] => 0
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2] => [2] => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [1] => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [3] => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1] => [1] => 0
([(3,6),(4,5)],7) => [1,1] => [1] => 0
([(2,3),(4,6),(5,6)],7) => [2,1] => [1] => 0
([(1,2),(3,6),(4,6),(5,6)],7) => [3,1] => [1] => 0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [4,1] => [1] => 0
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2] => [2] => 0
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [3,2] => [2] => 0
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [1,1] => 0
([(1,2),(3,6),(4,5),(5,6)],7) => [3,1] => [1] => 0
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [1,1] => 0
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [1] => 0
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,1] => [1] => 0
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,1] => [1] => 0
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 0
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [1] => 0
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [3,2] => [2] => 0
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2] => [2] => 0
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1] => [1] => 0
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,2] => [2] => 0
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 0
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 0
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 0
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [3] => 0
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,2] => [2] => 0
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [5,2] => [2] => 0
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,1] => [1] => 0
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,1] => 0
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [6,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,1] => [1] => 0
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 0
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 0
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 0
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 0
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 0
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 0
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [1] => 0
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => [1] => 0
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [1] => 0
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9,1] => [1] => 0
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [4,3] => [3] => 0
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,2] => [2] => 0
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => [3] => 0
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => [3] => 0
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [10,1] => [1] => 0
search for individual values
searching the database for the individual values of this statistic
Description
Twelve times the variance of the major index among all standard Young tableaux of a partition.
For a partition $\lambda$ of $n$, this variance is given in [1, Proposition 3.2] by
$$\frac{1}{12}\Big(\sum_{k = 1}^n i^2 - \sum_{i,j \in \lambda} h_{ij}^2\Big),$$
where the second sum ranges over all cells in $\lambda$ and $h_{ij}$ is the hook length of the cell $(i,j) \in \lambda$.
Map
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.
Map
first row removal
Description
Removes the first entry of an integer partition