Identifier
Values
([(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
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2] => [2] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [3] => 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
([(0,3),(1,2),(4,6),(5,6)],7) => [2,1,1] => [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
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,2] => [2] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3] => [3] => 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
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,1,1] => [1,1] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3] => [3] => 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 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
search for individual values
searching the database for the individual values of this statistic
Description
The Plancherel distribution on integer partitions.
This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions.
Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.
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.