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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001657
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001657: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001657: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
=> [2]
=> [1,1]
=> [1]
=> 0
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [5,1]
=> [1]
=> 0
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [2,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [4,1]
=> [1]
=> 0
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [2,2]
=> [2]
=> 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [2,1]
=> [1]
=> 0
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [2,1,1]
=> [1,1]
=> 0
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1]
=> [1,1]
=> 0
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,1]
=> [1]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [7,3]
=> [3]
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [3,2,2,2]
=> [2,2,2]
=> 3
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [6,3]
=> [3]
=> 0
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [3,2,2,1]
=> [2,2,1]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [4,1,1,1]
=> [1,1,1]
=> 0
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [7,2]
=> [2]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [6,2]
=> [2]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [4,4]
=> [4]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [5,2]
=> [2]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [4,1,1]
=> [1,1]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [3,2,1,1]
=> [2,1,1]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [3,3]
=> [3]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [3,1,1]
=> [1,1]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [3,1]
=> [1]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [7,1,1]
=> [1,1]
=> 0
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [2,2,2,2]
=> [2,2,2]
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [6,1,1]
=> [1,1]
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [2,2,2,1]
=> [2,2,1]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [2,2,2]
=> [2,2]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [7,1]
=> [1]
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [6,1]
=> [1]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [5,1,1]
=> [1,1]
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [5,1]
=> [1]
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [2,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [3,1,1,1]
=> [1,1,1]
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [4,1]
=> [1]
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [2,2]
=> [2]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [2,1]
=> [1]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [2,2,1,1]
=> [2,1,1]
=> 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [2,1,1,1]
=> [1,1,1]
=> 0
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [2,1,1]
=> [1,1]
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1]
=> [1,1,1]
=> 0
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1]
=> [1,1]
=> 0
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> [1,1]
=> [1]
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [9,5,1]
=> [5,1]
=> 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [5,2,2,2,2,1]
=> [2,2,2,2,1]
=> 4
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [8,5,1]
=> [5,1]
=> 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [7,2,2,2]
=> [2,2,2]
=> 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [6,2,1,1,1,1]
=> [2,1,1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [9,2,2,1]
=> [2,2,1]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [6,2,2,1,1,1]
=> [2,2,1,1,1]
=> 2
Description
The number of twos in an integer partition.
The total number of twos in all partitions of $n$ is equal to the total number of singletons [[St001484]] in all partitions of $n-1$, see [1].
Matching statistic: St000075
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 11%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 11%
Values
[1,1,0,0,1,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 0 + 2
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [[1,2,3,6],[4,5,7,8]]
=> ? = 1 + 2
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 0 + 2
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 2
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [[1,3,4,5,7,8,12],[2,6,9,10,11,13,14]]
=> ? = 0 + 2
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [[1,2,3,5,6,10],[4,7,8,9,11,12]]
=> ? = 3 + 2
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [[1,3,5,6,7,8,12],[2,4,9,10,11,13,14]]
=> ? = 0 + 2
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [[1,3,4,5,6,10],[2,7,8,9,11,12]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [[1,2,3,4,8],[5,6,7,9,10]]
=> ? = 0 + 2
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [[1,3,4,5,7,10,12],[2,6,8,9,11,13,14]]
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [[1,2,3,5,8,10],[4,6,7,9,11,12]]
=> ? = 1 + 2
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [[1,3,5,6,7,10,12],[2,4,8,9,11,13,14]]
=> ? = 0 + 2
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [[1,3,4,5,8,10],[2,6,7,9,11,12]]
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [[1,2,3,6,8],[4,5,7,9,10]]
=> ? = 0 + 2
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,3,5,7,8,10,12],[2,4,6,9,11,13,14]]
=> ? = 1 + 2
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [[1,3,5,6,8,10],[2,4,7,9,11,12]]
=> ? = 0 + 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[1,3,4,6,8],[2,5,7,9,10]]
=> ? = 0 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [[1,2,4,6],[3,5,7,8]]
=> ? = 0 + 2
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [[1,3,4,5,7,8],[2,6,9,10,11,12]]
=> ? = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [[1,2,3,5,6],[4,7,8,9,10]]
=> ? = 3 + 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [[1,3,5,6,7,8],[2,4,9,10,11,12]]
=> ? = 0 + 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [[1,3,4,5,6],[2,7,8,9,10]]
=> ? = 2 + 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [[1,2,3,4],[5,6,7,8]]
=> ? = 2 + 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [[1,3,4,5,7,10],[2,6,8,9,11,12]]
=> ? = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [[1,2,3,5,8],[4,6,7,9,10]]
=> ? = 0 + 2
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [[1,3,5,6,7,10],[2,4,8,9,11,12]]
=> ? = 0 + 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 0 + 2
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [[1,2,3,6],[4,5,7,8]]
=> ? = 1 + 2
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,7,8,10],[2,4,6,9,11,12]]
=> ? = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [[1,3,5,6,8],[2,4,7,9,10]]
=> ? = 0 + 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [[1,3,5,6,7],[2,4,8,9,10]]
=> ? = 1 + 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [[1,3,5,7,8],[2,4,6,9,10]]
=> ? = 0 + 2
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[1,3,4,5,7,8,9,12,16],[2,6,10,11,13,14,15,17,18]]
=> ? = 0 + 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[1,2,3,5,6,7,10,14],[4,8,9,11,12,13,15,16]]
=> ? = 4 + 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[1,3,5,6,7,8,9,12,16],[2,4,10,11,13,14,15,17,18]]
=> ? = 0 + 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[1,3,4,5,6,7,10,14],[2,8,9,11,12,13,15,16]]
=> ? = 3 + 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]]
=> ? = 1 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,4,5,7,9,10,12,16],[2,6,8,11,13,14,15,17,18]]
=> ? = 2 + 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [[1,2,3,5,7,8,10,14],[4,6,9,11,12,13,15,16]]
=> ? = 2 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,5,6,7,9,10,12,16],[2,4,8,11,13,14,15,17,18]]
=> ? = 0 + 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,4,5,7,8,10,14],[2,6,9,11,12,13,15,16]]
=> ? = 2 + 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [[1,2,3,5,6,8,12],[4,7,9,10,11,13,14]]
=> ? = 1 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,5,7,8,9,10,12,16],[2,4,6,11,13,14,15,17,18]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,5,6,7,8,10,14],[2,4,9,11,12,13,15,16]]
=> ? = 0 + 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [[1,3,4,5,6,8,12],[2,7,9,10,11,13,14]]
=> ? = 1 + 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [[1,2,3,4,6,10],[5,7,8,9,11,12]]
=> ? = 0 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
=> [2]
=> [1,0,1,0]
=> [[1,3],[2,4]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [[1,2,4],[3,5,6]]
=> 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
=> [3]
=> [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
Description
The orbit size of a standard tableau under promotion.
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