Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000698
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000698: 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]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
[[2],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2],[2],[2]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,1],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,1],[1,1],[1],[1]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[1,1],[1,1],[1,1]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[3],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 2
[[2],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
[[2],[2],[1],[1],[1]]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[2],[2],[2],[1]]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 0
[[1,1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
[[1,1],[1,1],[1],[1],[1]]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[1,1],[1,1],[1,1],[1]]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 0
[[3],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[3],[2],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[3],[2],[2]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 1
[[2,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2,1],[2],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1],[2],[2]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 1
[[2,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1],[1,1],[1,1]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 1
[[1,1,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,1,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[1,1,1],[1,1],[1,1]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 1
[[4],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[3,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,2],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 3
[[2],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 2
[[2],[2],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 2
[[2],[2],[2],[1],[1]]
 => [2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => 2
[[2],[2],[2],[2]]
 => [2,2,2,2]
 => [2,2,2]
 => [2,2]
 => 2
[[1,1],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 2
[[1,1],[1,1],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 2
[[1,1],[1,1],[1,1],[1],[1]]
 => [2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => 2
[[1,1],[1,1],[1,1],[1,1]]
 => [2,2,2,2]
 => [2,2,2]
 => [2,2]
 => 2
[[3],[1],[1],[1],[1],[1]]
 => [3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
[[3],[2],[1],[1],[1]]
 => [3,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[3],[2],[2],[1]]
 => [3,2,2,1]
 => [2,2,1]
 => [2,1]
 => 0
[[3],[3],[1],[1]]
 => [3,3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
Description
The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. For any positive integer $k$, one associates a $k$-core to a partition by repeatedly removing all rim hooks of size $k$. This statistic counts the $2$-rim hooks that are removed in this process to obtain a $2$-core.