Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000143
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000143: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1]
 => [1]
 => 0
[[1],[1]]
 => [1,1]
 => [2]
 => 0
[[2]]
 => [2]
 => [1,1]
 => 1
[[1,1]]
 => [2]
 => [1,1]
 => 1
[[1],[1],[1]]
 => [1,1,1]
 => [3]
 => 0
[[2],[1]]
 => [2,1]
 => [2,1]
 => 0
[[1,1],[1]]
 => [2,1]
 => [2,1]
 => 0
[[3]]
 => [3]
 => [1,1,1]
 => 1
[[2,1]]
 => [3]
 => [1,1,1]
 => 1
[[1,1,1]]
 => [3]
 => [1,1,1]
 => 1
[[1],[1],[1],[1]]
 => [1,1,1,1]
 => [4]
 => 0
[[2],[1],[1]]
 => [2,1,1]
 => [3,1]
 => 0
[[2],[2]]
 => [2,2]
 => [2,2]
 => 2
[[1,1],[1],[1]]
 => [2,1,1]
 => [3,1]
 => 0
[[1,1],[1,1]]
 => [2,2]
 => [2,2]
 => 2
[[3],[1]]
 => [3,1]
 => [2,1,1]
 => 1
[[2,1],[1]]
 => [3,1]
 => [2,1,1]
 => 1
[[1,1,1],[1]]
 => [3,1]
 => [2,1,1]
 => 1
[[4]]
 => [4]
 => [1,1,1,1]
 => 1
[[3,1]]
 => [4]
 => [1,1,1,1]
 => 1
[[2,2]]
 => [4]
 => [1,1,1,1]
 => 1
[[2,1,1]]
 => [4]
 => [1,1,1,1]
 => 1
[[1,1,1,1]]
 => [4]
 => [1,1,1,1]
 => 1
[[1],[1],[1],[1],[1]]
 => [1,1,1,1,1]
 => [5]
 => 0
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => 0
[[2],[2],[1]]
 => [2,2,1]
 => [3,2]
 => 0
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => 0
[[1,1],[1,1],[1]]
 => [2,2,1]
 => [3,2]
 => 0
[[3],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 1
[[3],[2]]
 => [3,2]
 => [2,2,1]
 => 2
[[2,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 1
[[2,1],[2]]
 => [3,2]
 => [2,2,1]
 => 2
[[2,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => 2
[[1,1,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 1
[[1,1,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => 2
[[4],[1]]
 => [4,1]
 => [2,1,1,1]
 => 1
[[3,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 1
[[2,2],[1]]
 => [4,1]
 => [2,1,1,1]
 => 1
[[2,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 1
[[1,1,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 1
[[5]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[4,1]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[3,2]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[3,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[2,2,1]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[2,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[1,1,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 1
[[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]
 => 0
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [4,2]
 => 0
Description
The largest repeated part of a partition. If the parts of the partition are all distinct, the value of the statistic is defined to be zero.
Matching statistic: St001587
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St001587: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1]
 => [1]
 => [1]
 => 0
[[1],[1]]
 => [1,1]
 => [2]
 => [1,1]
 => 0
[[2]]
 => [2]
 => [1,1]
 => [2]
 => 1
[[1,1]]
 => [2]
 => [1,1]
 => [2]
 => 1
[[1],[1],[1]]
 => [1,1,1]
 => [3]
 => [3]
 => 0
[[2],[1]]
 => [2,1]
 => [2,1]
 => [1,1,1]
 => 0
[[1,1],[1]]
 => [2,1]
 => [2,1]
 => [1,1,1]
 => 0
[[3]]
 => [3]
 => [1,1,1]
 => [2,1]
 => 1
[[2,1]]
 => [3]
 => [1,1,1]
 => [2,1]
 => 1
[[1,1,1]]
 => [3]
 => [1,1,1]
 => [2,1]
 => 1
[[1],[1],[1],[1]]
 => [1,1,1,1]
 => [4]
 => [1,1,1,1]
 => 0
[[2],[1],[1]]
 => [2,1,1]
 => [3,1]
 => [3,1]
 => 0
[[2],[2]]
 => [2,2]
 => [2,2]
 => [4]
 => 2
[[1,1],[1],[1]]
 => [2,1,1]
 => [3,1]
 => [3,1]
 => 0
[[1,1],[1,1]]
 => [2,2]
 => [2,2]
 => [4]
 => 2
[[3],[1]]
 => [3,1]
 => [2,1,1]
 => [2,1,1]
 => 1
[[2,1],[1]]
 => [3,1]
 => [2,1,1]
 => [2,1,1]
 => 1
[[1,1,1],[1]]
 => [3,1]
 => [2,1,1]
 => [2,1,1]
 => 1
[[4]]
 => [4]
 => [1,1,1,1]
 => [2,2]
 => 1
[[3,1]]
 => [4]
 => [1,1,1,1]
 => [2,2]
 => 1
[[2,2]]
 => [4]
 => [1,1,1,1]
 => [2,2]
 => 1
[[2,1,1]]
 => [4]
 => [1,1,1,1]
 => [2,2]
 => 1
[[1,1,1,1]]
 => [4]
 => [1,1,1,1]
 => [2,2]
 => 1
[[1],[1],[1],[1],[1]]
 => [1,1,1,1,1]
 => [5]
 => [5]
 => 0
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => [1,1,1,1,1]
 => 0
[[2],[2],[1]]
 => [2,2,1]
 => [3,2]
 => [3,1,1]
 => 0
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => [1,1,1,1,1]
 => 0
[[1,1],[1,1],[1]]
 => [2,2,1]
 => [3,2]
 => [3,1,1]
 => 0
[[3],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => [3,2]
 => 1
[[3],[2]]
 => [3,2]
 => [2,2,1]
 => [4,1]
 => 2
[[2,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => [3,2]
 => 1
[[2,1],[2]]
 => [3,2]
 => [2,2,1]
 => [4,1]
 => 2
[[2,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => [4,1]
 => 2
[[1,1,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => [3,2]
 => 1
[[1,1,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => [4,1]
 => 2
[[4],[1]]
 => [4,1]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[[3,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[[2,2],[1]]
 => [4,1]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[[2,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[[1,1,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => [2,1,1,1]
 => 1
[[5]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[4,1]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[3,2]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[3,1,1]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[2,2,1]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[2,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[1,1,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => [2,2,1]
 => 1
[[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1]
 => [6]
 => [3,3]
 => 0
[[2],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [5,1]
 => [5,1]
 => 0
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [4,2]
 => [1,1,1,1,1,1]
 => 0
Description
Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].