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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001448
St001448: Plane partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> 1
[[1],[1]]
=> 2
[[2]]
=> 0
[[1,1]]
=> 2
[[1],[1],[1]]
=> 3
[[2],[1]]
=> 1
[[1,1],[1]]
=> 3
[[3]]
=> 1
[[2,1]]
=> 1
[[1,1,1]]
=> 3
[[1],[1],[1],[1]]
=> 4
[[2],[1],[1]]
=> 2
[[2],[2]]
=> 0
[[1,1],[1],[1]]
=> 4
[[1,1],[1,1]]
=> 4
[[3],[1]]
=> 2
[[2,1],[1]]
=> 2
[[1,1,1],[1]]
=> 4
[[4]]
=> 0
[[3,1]]
=> 2
[[2,2]]
=> 0
[[2,1,1]]
=> 2
[[1,1,1,1]]
=> 4
[[1],[1],[1],[1],[1]]
=> 5
[[2],[1],[1],[1]]
=> 3
[[2],[2],[1]]
=> 1
[[1,1],[1],[1],[1]]
=> 5
[[1,1],[1,1],[1]]
=> 5
[[3],[1],[1]]
=> 3
[[3],[2]]
=> 1
[[2,1],[1],[1]]
=> 3
[[2,1],[2]]
=> 1
[[2,1],[1,1]]
=> 3
[[1,1,1],[1],[1]]
=> 5
[[1,1,1],[1,1]]
=> 5
[[4],[1]]
=> 1
[[3,1],[1]]
=> 3
[[2,2],[1]]
=> 1
[[2,1,1],[1]]
=> 3
[[1,1,1,1],[1]]
=> 5
[[5]]
=> 1
[[4,1]]
=> 1
[[3,2]]
=> 1
[[3,1,1]]
=> 3
[[2,2,1]]
=> 1
[[2,1,1,1]]
=> 3
[[1,1,1,1,1]]
=> 5
[[1],[1],[1],[1],[1],[1]]
=> 6
[[2],[1],[1],[1],[1]]
=> 4
[[2],[2],[1],[1]]
=> 2
Description
Number of odd parts in a plane partition.
Matching statistic: St000992
Mp00311: Plane partitions —to partition⟶ Integer partitions
St000992: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000992: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1]
=> 1
[[1],[1]]
=> [1,1]
=> 0
[[2]]
=> [2]
=> 2
[[1,1]]
=> [2]
=> 2
[[1],[1],[1]]
=> [1,1,1]
=> 1
[[2],[1]]
=> [2,1]
=> 1
[[1,1],[1]]
=> [2,1]
=> 1
[[3]]
=> [3]
=> 3
[[2,1]]
=> [3]
=> 3
[[1,1,1]]
=> [3]
=> 3
[[1],[1],[1],[1]]
=> [1,1,1,1]
=> 0
[[2],[1],[1]]
=> [2,1,1]
=> 2
[[2],[2]]
=> [2,2]
=> 0
[[1,1],[1],[1]]
=> [2,1,1]
=> 2
[[1,1],[1,1]]
=> [2,2]
=> 0
[[3],[1]]
=> [3,1]
=> 2
[[2,1],[1]]
=> [3,1]
=> 2
[[1,1,1],[1]]
=> [3,1]
=> 2
[[4]]
=> [4]
=> 4
[[3,1]]
=> [4]
=> 4
[[2,2]]
=> [4]
=> 4
[[2,1,1]]
=> [4]
=> 4
[[1,1,1,1]]
=> [4]
=> 4
[[1],[1],[1],[1],[1]]
=> [1,1,1,1,1]
=> 1
[[2],[1],[1],[1]]
=> [2,1,1,1]
=> 1
[[2],[2],[1]]
=> [2,2,1]
=> 1
[[1,1],[1],[1],[1]]
=> [2,1,1,1]
=> 1
[[1,1],[1,1],[1]]
=> [2,2,1]
=> 1
[[3],[1],[1]]
=> [3,1,1]
=> 3
[[3],[2]]
=> [3,2]
=> 1
[[2,1],[1],[1]]
=> [3,1,1]
=> 3
[[2,1],[2]]
=> [3,2]
=> 1
[[2,1],[1,1]]
=> [3,2]
=> 1
[[1,1,1],[1],[1]]
=> [3,1,1]
=> 3
[[1,1,1],[1,1]]
=> [3,2]
=> 1
[[4],[1]]
=> [4,1]
=> 3
[[3,1],[1]]
=> [4,1]
=> 3
[[2,2],[1]]
=> [4,1]
=> 3
[[2,1,1],[1]]
=> [4,1]
=> 3
[[1,1,1,1],[1]]
=> [4,1]
=> 3
[[5]]
=> [5]
=> 5
[[4,1]]
=> [5]
=> 5
[[3,2]]
=> [5]
=> 5
[[3,1,1]]
=> [5]
=> 5
[[2,2,1]]
=> [5]
=> 5
[[2,1,1,1]]
=> [5]
=> 5
[[1,1,1,1,1]]
=> [5]
=> 5
[[1],[1],[1],[1],[1],[1]]
=> [1,1,1,1,1,1]
=> 0
[[2],[1],[1],[1],[1]]
=> [2,1,1,1,1]
=> 2
[[2],[2],[1],[1]]
=> [2,2,1,1]
=> 0
Description
The alternating sum of the parts of an integer partition.
For a partition $\lambda = (\lambda_1,\ldots,\lambda_k)$, this is $\lambda_1 - \lambda_2 + \cdots \pm \lambda_k$.
Matching statistic: St000148
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Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000148: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000148: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1]
=> [1]
=> 1
[[1],[1]]
=> [1,1]
=> [2]
=> 0
[[2]]
=> [2]
=> [1,1]
=> 2
[[1,1]]
=> [2]
=> [1,1]
=> 2
[[1],[1],[1]]
=> [1,1,1]
=> [3]
=> 1
[[2],[1]]
=> [2,1]
=> [2,1]
=> 1
[[1,1],[1]]
=> [2,1]
=> [2,1]
=> 1
[[3]]
=> [3]
=> [1,1,1]
=> 3
[[2,1]]
=> [3]
=> [1,1,1]
=> 3
[[1,1,1]]
=> [3]
=> [1,1,1]
=> 3
[[1],[1],[1],[1]]
=> [1,1,1,1]
=> [4]
=> 0
[[2],[1],[1]]
=> [2,1,1]
=> [3,1]
=> 2
[[2],[2]]
=> [2,2]
=> [2,2]
=> 0
[[1,1],[1],[1]]
=> [2,1,1]
=> [3,1]
=> 2
[[1,1],[1,1]]
=> [2,2]
=> [2,2]
=> 0
[[3],[1]]
=> [3,1]
=> [2,1,1]
=> 2
[[2,1],[1]]
=> [3,1]
=> [2,1,1]
=> 2
[[1,1,1],[1]]
=> [3,1]
=> [2,1,1]
=> 2
[[4]]
=> [4]
=> [1,1,1,1]
=> 4
[[3,1]]
=> [4]
=> [1,1,1,1]
=> 4
[[2,2]]
=> [4]
=> [1,1,1,1]
=> 4
[[2,1,1]]
=> [4]
=> [1,1,1,1]
=> 4
[[1,1,1,1]]
=> [4]
=> [1,1,1,1]
=> 4
[[1],[1],[1],[1],[1]]
=> [1,1,1,1,1]
=> [5]
=> 1
[[2],[1],[1],[1]]
=> [2,1,1,1]
=> [4,1]
=> 1
[[2],[2],[1]]
=> [2,2,1]
=> [3,2]
=> 1
[[1,1],[1],[1],[1]]
=> [2,1,1,1]
=> [4,1]
=> 1
[[1,1],[1,1],[1]]
=> [2,2,1]
=> [3,2]
=> 1
[[3],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 3
[[3],[2]]
=> [3,2]
=> [2,2,1]
=> 1
[[2,1],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 3
[[2,1],[2]]
=> [3,2]
=> [2,2,1]
=> 1
[[2,1],[1,1]]
=> [3,2]
=> [2,2,1]
=> 1
[[1,1,1],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 3
[[1,1,1],[1,1]]
=> [3,2]
=> [2,2,1]
=> 1
[[4],[1]]
=> [4,1]
=> [2,1,1,1]
=> 3
[[3,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 3
[[2,2],[1]]
=> [4,1]
=> [2,1,1,1]
=> 3
[[2,1,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 3
[[1,1,1,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 3
[[5]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[4,1]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[3,2]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[3,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[2,2,1]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[2,1,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[1,1,1,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 5
[[1],[1],[1],[1],[1],[1]]
=> [1,1,1,1,1,1]
=> [6]
=> 0
[[2],[1],[1],[1],[1]]
=> [2,1,1,1,1]
=> [5,1]
=> 2
[[2],[2],[1],[1]]
=> [2,2,1,1]
=> [4,2]
=> 0
Description
The number of odd parts of a partition.
Matching statistic: St000022
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000022: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000022: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1]
=> [[1]]
=> [1] => 1
[[1],[1]]
=> [1,1]
=> [[1],[2]]
=> [2,1] => 0
[[2]]
=> [2]
=> [[1,2]]
=> [1,2] => 2
[[1,1]]
=> [2]
=> [[1,2]]
=> [1,2] => 2
[[1],[1],[1]]
=> [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 1
[[2],[1]]
=> [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 1
[[1,1],[1]]
=> [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 1
[[3]]
=> [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[[2,1]]
=> [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[[1,1,1]]
=> [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[[1],[1],[1],[1]]
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => 0
[[2],[1],[1]]
=> [2,1,1]
=> [[1,4],[2],[3]]
=> [3,2,1,4] => 2
[[2],[2]]
=> [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 0
[[1,1],[1],[1]]
=> [2,1,1]
=> [[1,4],[2],[3]]
=> [3,2,1,4] => 2
[[1,1],[1,1]]
=> [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 0
[[3],[1]]
=> [3,1]
=> [[1,3,4],[2]]
=> [2,1,3,4] => 2
[[2,1],[1]]
=> [3,1]
=> [[1,3,4],[2]]
=> [2,1,3,4] => 2
[[1,1,1],[1]]
=> [3,1]
=> [[1,3,4],[2]]
=> [2,1,3,4] => 2
[[4]]
=> [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 4
[[3,1]]
=> [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 4
[[2,2]]
=> [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 4
[[2,1,1]]
=> [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 4
[[1,1,1,1]]
=> [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 4
[[1],[1],[1],[1],[1]]
=> [1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => 1
[[2],[1],[1],[1]]
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 1
[[2],[2],[1]]
=> [2,2,1]
=> [[1,3],[2,5],[4]]
=> [4,2,5,1,3] => 1
[[1,1],[1],[1],[1]]
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 1
[[1,1],[1,1],[1]]
=> [2,2,1]
=> [[1,3],[2,5],[4]]
=> [4,2,5,1,3] => 1
[[3],[1],[1]]
=> [3,1,1]
=> [[1,4,5],[2],[3]]
=> [3,2,1,4,5] => 3
[[3],[2]]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [3,4,1,2,5] => 1
[[2,1],[1],[1]]
=> [3,1,1]
=> [[1,4,5],[2],[3]]
=> [3,2,1,4,5] => 3
[[2,1],[2]]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [3,4,1,2,5] => 1
[[2,1],[1,1]]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [3,4,1,2,5] => 1
[[1,1,1],[1],[1]]
=> [3,1,1]
=> [[1,4,5],[2],[3]]
=> [3,2,1,4,5] => 3
[[1,1,1],[1,1]]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [3,4,1,2,5] => 1
[[4],[1]]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [2,1,3,4,5] => 3
[[3,1],[1]]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [2,1,3,4,5] => 3
[[2,2],[1]]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [2,1,3,4,5] => 3
[[2,1,1],[1]]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [2,1,3,4,5] => 3
[[1,1,1,1],[1]]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [2,1,3,4,5] => 3
[[5]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[4,1]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[3,2]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[3,1,1]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[2,2,1]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[2,1,1,1]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[1,1,1,1,1]]
=> [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 5
[[1],[1],[1],[1],[1],[1]]
=> [1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => 0
[[2],[1],[1],[1],[1]]
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 2
[[2],[2],[1],[1]]
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 0
Description
The number of fixed points of a permutation.
Matching statistic: St000288
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St000288: Binary words ⟶ ℤResult quality: 91% ●values known / values provided: 96%●distinct values known / distinct values provided: 91%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St000288: Binary words ⟶ ℤResult quality: 91% ●values known / values provided: 96%●distinct values known / distinct values provided: 91%
Values
[[1]]
=> [1]
=> [1]
=> 1 => 1
[[1],[1]]
=> [1,1]
=> [2]
=> 0 => 0
[[2]]
=> [2]
=> [1,1]
=> 11 => 2
[[1,1]]
=> [2]
=> [1,1]
=> 11 => 2
[[1],[1],[1]]
=> [1,1,1]
=> [3]
=> 1 => 1
[[2],[1]]
=> [2,1]
=> [2,1]
=> 01 => 1
[[1,1],[1]]
=> [2,1]
=> [2,1]
=> 01 => 1
[[3]]
=> [3]
=> [1,1,1]
=> 111 => 3
[[2,1]]
=> [3]
=> [1,1,1]
=> 111 => 3
[[1,1,1]]
=> [3]
=> [1,1,1]
=> 111 => 3
[[1],[1],[1],[1]]
=> [1,1,1,1]
=> [4]
=> 0 => 0
[[2],[1],[1]]
=> [2,1,1]
=> [3,1]
=> 11 => 2
[[2],[2]]
=> [2,2]
=> [2,2]
=> 00 => 0
[[1,1],[1],[1]]
=> [2,1,1]
=> [3,1]
=> 11 => 2
[[1,1],[1,1]]
=> [2,2]
=> [2,2]
=> 00 => 0
[[3],[1]]
=> [3,1]
=> [2,1,1]
=> 011 => 2
[[2,1],[1]]
=> [3,1]
=> [2,1,1]
=> 011 => 2
[[1,1,1],[1]]
=> [3,1]
=> [2,1,1]
=> 011 => 2
[[4]]
=> [4]
=> [1,1,1,1]
=> 1111 => 4
[[3,1]]
=> [4]
=> [1,1,1,1]
=> 1111 => 4
[[2,2]]
=> [4]
=> [1,1,1,1]
=> 1111 => 4
[[2,1,1]]
=> [4]
=> [1,1,1,1]
=> 1111 => 4
[[1,1,1,1]]
=> [4]
=> [1,1,1,1]
=> 1111 => 4
[[1],[1],[1],[1],[1]]
=> [1,1,1,1,1]
=> [5]
=> 1 => 1
[[2],[1],[1],[1]]
=> [2,1,1,1]
=> [4,1]
=> 01 => 1
[[2],[2],[1]]
=> [2,2,1]
=> [3,2]
=> 10 => 1
[[1,1],[1],[1],[1]]
=> [2,1,1,1]
=> [4,1]
=> 01 => 1
[[1,1],[1,1],[1]]
=> [2,2,1]
=> [3,2]
=> 10 => 1
[[3],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 111 => 3
[[3],[2]]
=> [3,2]
=> [2,2,1]
=> 001 => 1
[[2,1],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 111 => 3
[[2,1],[2]]
=> [3,2]
=> [2,2,1]
=> 001 => 1
[[2,1],[1,1]]
=> [3,2]
=> [2,2,1]
=> 001 => 1
[[1,1,1],[1],[1]]
=> [3,1,1]
=> [3,1,1]
=> 111 => 3
[[1,1,1],[1,1]]
=> [3,2]
=> [2,2,1]
=> 001 => 1
[[4],[1]]
=> [4,1]
=> [2,1,1,1]
=> 0111 => 3
[[3,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 0111 => 3
[[2,2],[1]]
=> [4,1]
=> [2,1,1,1]
=> 0111 => 3
[[2,1,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 0111 => 3
[[1,1,1,1],[1]]
=> [4,1]
=> [2,1,1,1]
=> 0111 => 3
[[5]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[4,1]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[3,2]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[3,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[2,2,1]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[2,1,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[1,1,1,1,1]]
=> [5]
=> [1,1,1,1,1]
=> 11111 => 5
[[1],[1],[1],[1],[1],[1]]
=> [1,1,1,1,1,1]
=> [6]
=> 0 => 0
[[2],[1],[1],[1],[1]]
=> [2,1,1,1,1]
=> [5,1]
=> 11 => 2
[[2],[2],[1],[1]]
=> [2,2,1,1]
=> [4,2]
=> 00 => 0
[[10]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[9,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[8,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[8,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[7,3]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[7,2,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[7,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[6,4]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[6,3,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[6,2,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[6,2,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[6,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,5]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,4,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,3,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,3,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,2,2,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,2,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[5,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,4,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,4,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,3,3]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,3,2,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,3,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,2,2,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,2,2,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,2,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[4,1,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,3,3,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,3,2,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,3,2,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,3,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,2,2,2,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,2,2,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,2,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[3,1,1,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[2,2,2,2,2]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[2,2,2,2,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[2,2,2,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[2,2,1,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[2,1,1,1,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
[[1,1,1,1,1,1,1,1,1,1]]
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> 1111111111 => ? ∊ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
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