Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001914
Mapping
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001914: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1,1] => [1,1]
 => [1]
 => 1
[1,0,1,0,1,0]
 => [1,1,1] => [1,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,0]
 => [1,2] => [2,1]
 => [1]
 => 1
[1,1,0,0,1,0]
 => [2,1] => [2,1]
 => [1]
 => 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1] => [1,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,1,0,0]
 => [1,1,2] => [2,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,0]
 => [1,2,1] => [2,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,1,0,0]
 => [1,3] => [3,1]
 => [1]
 => 1
[1,0,1,1,1,0,0,0]
 => [1,3] => [3,1]
 => [1]
 => 1
[1,1,0,0,1,0,1,0]
 => [2,1,1] => [2,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0]
 => [2,2] => [2,2]
 => [2]
 => 2
[1,1,0,1,0,0,1,0]
 => [3,1] => [3,1]
 => [1]
 => 1
[1,1,1,0,0,0,1,0]
 => [3,1] => [3,1]
 => [1]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => [1,1,1,1,1]
 => [1,1,1,1]
 => 5
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => [2,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => [2,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => [3,1,1]
 => [1,1]
 => 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => [3,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [2,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => [2,2,1]
 => [2,1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [3,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,4] => [4,1]
 => [1]
 => 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,4] => [4,1]
 => [1]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [3,1,1]
 => [1,1]
 => 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,4] => [4,1]
 => [1]
 => 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4] => [4,1]
 => [1]
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,4] => [4,1]
 => [1]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [2,1,1,1]
 => [1,1,1]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [2,2,1]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [2,2,1]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,3] => [3,2]
 => [2]
 => 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,3] => [3,2]
 => [2]
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [3,1,1]
 => [1,1]
 => 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,2] => [3,2]
 => [2]
 => 2
[1,1,0,1,0,1,0,0,1,0]
 => [4,1] => [4,1]
 => [1]
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1] => [4,1]
 => [1]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [3,1,1]
 => [1,1]
 => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,2] => [3,2]
 => [2]
 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [4,1] => [4,1]
 => [1]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1] => [4,1]
 => [1]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,1] => [4,1]
 => [1]
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 6
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,2] => [2,1,1,1,1]
 => [1,1,1,1]
 => 5
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,2,1] => [2,1,1,1,1]
 => [1,1,1,1]
 => 5
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,3] => [3,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,3] => [3,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,2,1,1] => [2,1,1,1,1]
 => [1,1,1,1]
 => 5
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,2,2] => [2,2,1,1]
 => [2,1,1]
 => 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => [3,1,1,1]
 => [1,1,1]
 => 3
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,4] => [4,1,1]
 => [1,1]
 => 2
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.