Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001448
Mapping
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
Mapping
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%
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
(load all 2 compositions to match this statistic)
Mapping
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%
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
Mapping
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%
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
Mapping
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: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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
Description
The number of ones in a binary word. This is also known as the Hamming weight of the word.
Matching statistic: St001372
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St001372: Binary words ⟶ 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]
 => [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
Description
The length of a longest cyclic run of ones of a binary word. Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.