Identifier
Values
([(0,3),(1,2)],4) => [1,1] => [1] => 1
([(1,4),(2,3)],5) => [1,1] => [1] => 1
([(0,1),(2,4),(3,4)],5) => [2,1] => [1] => 1
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [1] => 1
([(2,5),(3,4)],6) => [1,1] => [1] => 1
([(1,2),(3,5),(4,5)],6) => [2,1] => [1] => 1
([(0,1),(2,5),(3,5),(4,5)],6) => [3,1] => [1] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2] => [2] => 1
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [1,1] => 1
([(0,1),(2,5),(3,4),(4,5)],6) => [3,1] => [1] => 1
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [1] => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,1] => [1] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [1] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2] => [2] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [1] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [3] => 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6,1] => [1] => 1
([(3,6),(4,5)],7) => [1,1] => [1] => 1
([(2,3),(4,6),(5,6)],7) => [2,1] => [1] => 1
([(1,2),(3,6),(4,6),(5,6)],7) => [3,1] => [1] => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [4,1] => [1] => 1
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2] => [2] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [3,2] => [2] => 1
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [1,1] => 1
([(1,2),(3,6),(4,5),(5,6)],7) => [3,1] => [1] => 1
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [1,1] => 1
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [1] => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,1] => [1] => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,1] => [1] => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [1] => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [3,2] => [2] => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2] => [2] => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1] => [1] => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,2] => [2] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [3] => 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [6,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,2] => [2] => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [5,2] => [2] => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,1] => [1] => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,1] => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [5,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [6,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,1] => [1] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 1
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => [1] => 1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [8,1] => [1] => 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7,1] => [1] => 1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [8,1] => [1] => 1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [9,1] => [1] => 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [4,3] => [3] => 1
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,2] => [2] => 1
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => [3] => 1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => [3] => 1
([(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] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition.
For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.