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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001919

Mapping

St001919: Plane partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[[1]]
 => 1
[[1],[1]]
 => 1
[[2]]
 => 2
[[1,1]]
 => 1
[[1],[1],[1]]
 => 1
[[2],[1]]
 => 2
[[1,1],[1]]
 => 1
[[3]]
 => 3
[[2,1]]
 => 2
[[1,1,1]]
 => 1
[[1],[1],[1],[1]]
 => 1
[[2],[1],[1]]
 => 2
[[2],[2]]
 => 2
[[1,1],[1],[1]]
 => 1
[[1,1],[1,1]]
 => 2
[[3],[1]]
 => 3
[[2,1],[1]]
 => 2
[[1,1,1],[1]]
 => 1
[[4]]
 => 4
[[3,1]]
 => 3
[[2,2]]
 => 2
[[2,1,1]]
 => 2
[[1,1,1,1]]
 => 1
[[1],[1],[1],[1],[1]]
 => 1
[[2],[1],[1],[1]]
 => 2
[[2],[2],[1]]
 => 2
[[1,1],[1],[1],[1]]
 => 1
[[1,1],[1,1],[1]]
 => 2
[[3],[1],[1]]
 => 3
[[3],[2]]
 => 3
[[2,1],[1],[1]]
 => 2
[[2,1],[2]]
 => 2
[[2,1],[1,1]]
 => 3
[[1,1,1],[1],[1]]
 => 1
[[1,1,1],[1,1]]
 => 2
[[4],[1]]
 => 4
[[3,1],[1]]
 => 3
[[2,2],[1]]
 => 2
[[2,1,1],[1]]
 => 2
[[1,1,1,1],[1]]
 => 1
[[5]]
 => 5
[[4,1]]
 => 4
[[3,2]]
 => 3
[[3,1,1]]
 => 3
[[2,2,1]]
 => 2
[[2,1,1,1]]
 => 2
[[1,1,1,1,1]]
 => 1
[[1],[1],[1],[1],[1],[1]]
 => 1
[[2],[1],[1],[1],[1]]
 => 2
[[2],[2],[1],[1]]
 => 2

Description

The trace of a plane partition. This is the sum of the diagonal entries

$\sum_i \lambda^{(i)}_i$ of a plane partition

$\Lambda=[\lambda^{(i)}_j]_{i,j}$ .

Matching statistic: St001923

Mapping

St001923: Plane partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[[1]]
 => 1
[[1],[1]]
 => 1
[[2]]
 => 1
[[1,1]]
 => 2
[[1],[1],[1]]
 => 1
[[2],[1]]
 => 1
[[1,1],[1]]
 => 2
[[3]]
 => 1
[[2,1]]
 => 2
[[1,1,1]]
 => 3
[[1],[1],[1],[1]]
 => 1
[[2],[1],[1]]
 => 1
[[2],[2]]
 => 2
[[1,1],[1],[1]]
 => 2
[[1,1],[1,1]]
 => 2
[[3],[1]]
 => 1
[[2,1],[1]]
 => 2
[[1,1,1],[1]]
 => 3
[[4]]
 => 1
[[3,1]]
 => 2
[[2,2]]
 => 2
[[2,1,1]]
 => 3
[[1,1,1,1]]
 => 4
[[1],[1],[1],[1],[1]]
 => 1
[[2],[1],[1],[1]]
 => 1
[[2],[2],[1]]
 => 2
[[1,1],[1],[1],[1]]
 => 2
[[1,1],[1,1],[1]]
 => 2
[[3],[1],[1]]
 => 1
[[3],[2]]
 => 2
[[2,1],[1],[1]]
 => 2
[[2,1],[2]]
 => 3
[[2,1],[1,1]]
 => 2
[[1,1,1],[1],[1]]
 => 3
[[1,1,1],[1,1]]
 => 3
[[4],[1]]
 => 1
[[3,1],[1]]
 => 2
[[2,2],[1]]
 => 2
[[2,1,1],[1]]
 => 3
[[1,1,1,1],[1]]
 => 4
[[5]]
 => 1
[[4,1]]
 => 2
[[3,2]]
 => 2
[[3,1,1]]
 => 3
[[2,2,1]]
 => 3
[[2,1,1,1]]
 => 4
[[1,1,1,1,1]]
 => 5
[[1],[1],[1],[1],[1],[1]]
 => 1
[[2],[1],[1],[1],[1]]
 => 1
[[2],[2],[1],[1]]
 => 2

Description

The conjugate trace of a plane partition. This is the number of parts satisfying

$\lambda^{(i)}_j \geq i$ .