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Matching statistic: St001914
Mapping
St001914: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 2
[2,1]
 => 1
[1,1,1]
 => 3
[4]
 => 4
[3,1]
 => 3
[2,2]
 => 3
[2,1,1]
 => 3
[1,1,1,1]
 => 5
[5]
 => 5
[4,1]
 => 4
[3,2]
 => 3
[3,1,1]
 => 3
[2,2,1]
 => 3
[2,1,1,1]
 => 5
[1,1,1,1,1]
 => 6
[6]
 => 4
[5,1]
 => 3
[4,2]
 => 2
[4,1,1]
 => 6
[3,3]
 => 5
[3,2,1]
 => 1
[3,1,1,1]
 => 3
[2,2,2]
 => 4
[2,2,1,1]
 => 7
[2,1,1,1,1]
 => 4
[1,1,1,1,1,1]
 => 5
[7]
 => 7
[6,1]
 => 6
[5,2]
 => 5
[5,1,1]
 => 6
[4,3]
 => 5
[4,2,1]
 => 4
[4,1,1,1]
 => 6
[3,3,1]
 => 4
[3,2,2]
 => 4
[3,2,1,1]
 => 4
[3,1,1,1,1]
 => 6
[2,2,2,1]
 => 7
[2,2,1,1,1]
 => 7
[2,1,1,1,1,1]
 => 7
[1,1,1,1,1,1,1]
 => 8
[8]
 => 8
[7,1]
 => 7
[6,2]
 => 6
[6,1,1]
 => 4
[5,3]
 => 3
[5,2,1]
 => 5
Description
The size of the orbit of an integer partition in Bulgarian solitaire. Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row. This statistic returns the number of partitions that can be obtained from the given partition.