Identifier
-
Mp00037:
Graphs
—to partition of connected components⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000284: Integer partitions ⟶ ℤ
Values
([],3) => [1,1,1] => [1,1] => 1
([],4) => [1,1,1,1] => [1,1,1] => 1
([(2,3)],4) => [2,1,1] => [1,1] => 1
([(0,3),(1,2)],4) => [2,2] => [2] => 1
([],5) => [1,1,1,1,1] => [1,1,1,1] => 1
([(3,4)],5) => [2,1,1,1] => [1,1,1] => 1
([(2,4),(3,4)],5) => [3,1,1] => [1,1] => 1
([(1,4),(2,3)],5) => [2,2,1] => [2,1] => 4
([(0,1),(2,4),(3,4)],5) => [3,2] => [2] => 1
([(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,1] => 1
([(0,1),(2,3),(2,4),(3,4)],5) => [3,2] => [2] => 1
([],6) => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
([(4,5)],6) => [2,1,1,1,1] => [1,1,1,1] => 1
([(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 1
([(2,5),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
([(2,5),(3,4)],6) => [2,2,1,1] => [2,1,1] => 9
([(2,5),(3,4),(4,5)],6) => [4,1,1] => [1,1] => 1
([(1,2),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 4
([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [1,1,1] => 1
([(0,1),(2,5),(3,5),(4,5)],6) => [4,2] => [2] => 1
([(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
([(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1] => [1,1] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,1] => 1
([(0,5),(1,4),(2,3)],6) => [2,2,2] => [2,2] => 4
([(0,1),(2,5),(3,4),(4,5)],6) => [4,2] => [2] => 1
([(1,2),(3,4),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,3] => [3] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2] => 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [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) => [4,2] => [2] => 1
([],7) => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
([(5,6)],7) => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
([(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 1
([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(3,6),(4,5)],7) => [2,2,1,1,1] => [2,1,1,1] => 16
([(3,6),(4,5),(5,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(2,3),(4,6),(5,6)],7) => [3,2,1,1] => [2,1,1] => 9
([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => [1,1,1,1] => 1
([(2,6),(3,6),(4,5),(5,6)],7) => [5,1,1] => [1,1] => 1
([(1,2),(3,6),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 4
([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(3,5),(3,6),(4,5),(4,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(1,6),(2,6),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 9
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1] => [1,1] => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(1,6),(2,5),(3,4)],7) => [2,2,2,1] => [2,2,1] => 25
([(2,6),(3,5),(4,5),(4,6)],7) => [5,1,1] => [1,1] => 1
([(1,2),(3,6),(4,5),(5,6)],7) => [4,2,1] => [2,1] => 4
([(0,3),(1,2),(4,6),(5,6)],7) => [3,2,2] => [2,2] => 4
([(2,3),(4,5),(4,6),(5,6)],7) => [3,2,1,1] => [2,1,1] => 9
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2] => [2] => 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,1,1] => [1,1] => 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,1] => [2,1] => 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 9
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2] => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 4
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [4,3] => [3] => 1
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,1,1] => 1
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2] => 1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [5,1,1] => [1,1] => 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3] => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [4,3] => [3] => 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,1] => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,2,2] => [2,2] => 4
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,2] => [2] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3,1] => [3,1] => 9
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 1
>>> Load all 216 entries. <<<
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.
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
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!