Identifier
-
Mp00037:
Graphs
—to partition of connected components⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000708: 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] => 2
([],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] => 2
([(0,1),(2,4),(3,4)],5) => [3,2] => [2] => 2
([(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] => 2
([],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] => 2
([(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] => 2
([(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] => 2
([(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] => 3
([(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] => 2
([(1,2),(3,4),(3,5),(4,5)],6) => [3,2,1] => [2,1] => 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2] => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2] => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,3] => [3] => 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2] => 2
([(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] => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2] => 2
([],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] => 2
([(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] => 2
([(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] => 2
([(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] => 2
([(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] => 3
([(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] => 3
([(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] => 4
([(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] => 2
([(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] => 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [5,2] => [2] => 2
([(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] => 2
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(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] => 2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,3,1] => [3,1] => 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2] => 2
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 3
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => [2,1] => 2
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [4,3] => [3] => 3
([(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] => 2
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(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] => 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [4,3] => [3] => 3
([(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] => 2
([(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] => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5,2] => [2] => 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [4,3] => [3] => 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3,1] => [3,1] => 3
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [2] => 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [4,3] => [3] => 3
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search for individual values
searching the database for the individual values of this statistic
Description
The product of the parts of an integer partition.
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
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