- FindStat

Identifier

Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000382: Integer compositions ⟶ ℤ

Values

[[1]] => [1] => [[1]] => [1] => 1

[[1],[1]] => [1,1] => [[1],[2]] => [1,1] => 1

[[2]] => [2] => [[1,2]] => [2] => 2

[[1,1]] => [2] => [[1,2]] => [2] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 1

[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 2

[[2],[2],[1],[1]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2

[[2],[2],[2]] => [2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 2

[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 2

[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 2

[[1,1],[1,1],[1,1]] => [2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 2

[[3],[1],[1],[1]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3

[[3],[2],[1]] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 3

[[3],[3]] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 3

[[2,1],[1],[1],[1]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3

[[2,1],[2],[1]] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 3

[[2,1],[1,1],[1]] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 3

[[2,1],[2,1]] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 3

[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 3

[[1,1,1],[1,1],[1]] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 3

[[1,1,1],[1,1,1]] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 3

[[4],[1],[1]] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 4

[[4],[2]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[3,1],[1],[1]] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 4

[[3,1],[2]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[3,1],[1,1]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[2,2],[1],[1]] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 4

[[2,2],[2]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[2,2],[1,1]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[2,1,1],[1],[1]] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 4

[[2,1,1],[2]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[2,1,1],[1,1]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[1,1,1,1],[1],[1]] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 4

[[1,1,1,1],[1,1]] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 4

[[5],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[4,1],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[3,2],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[3,1,1],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[2,2,1],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[2,1,1,1],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[1,1,1,1,1],[1]] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 5

[[6]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[5,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[4,2]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[4,1,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[3,3]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[3,2,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[3,1,1,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[2,2,2]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[2,2,1,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[2,1,1,1,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[1,1,1,1,1,1]] => [6] => [[1,2,3,4,5,6]] => [6] => 6

[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 1

[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 2

[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 2

[[2],[2],[2],[1]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 2

[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 2

[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 2

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Description

The first part of an integer composition.

Map

to partition

Description

The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.

Map

horizontal strip sizes

Description

The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.

Map

initial tableau

Description

Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.