- FindStat

Identifier

Mp00177: Plane partitions —transpose⟶ Plane partitions
St001460: Plane partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

[[3]] => [[3]] => 1

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

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

[[1],[1],[1],[1]] => [[1,1,1,1]] => 4

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

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

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

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

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

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

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

[[4]] => [[4]] => 1

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

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

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

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

[[1],[1],[1],[1],[1]] => [[1,1,1,1,1]] => 5

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

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

[[1,1],[1],[1],[1]] => [[1,1,1,1],[1]] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5]] => [[5]] => 1

[[4,1]] => [[4],[1]] => 1

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

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

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

[[2,1,1,1]] => [[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]] => 6

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

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

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

[[1,1],[1],[1],[1],[1]] => [[1,1,1,1,1],[1]] => 5

[[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]] => 3

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

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

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

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

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

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

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

[[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]] => 3

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

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

[[4],[2]] => [[4,2]] => 2

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

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

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

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

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

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

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

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

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

[[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]] => 2

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

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

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

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

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

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

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

[[6]] => [[6]] => 1

[[5,1]] => [[5],[1]] => 1

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

[[4,1,1]] => [[4],[1],[1]] => 1

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

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

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

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

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

[[2,1,1,1,1]] => [[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]] => [[1,1,1,1,1,1,1]] => 7

[[2],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1]] => 6

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

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

[[1,1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1],[1]] => 6

[[1,1],[1,1],[1],[1],[1]] => [[1,1,1,1,1],[1,1]] => 5

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$F_{1} = q$

$F_{2} = 2\ q + q^{2}$

$F_{3} = 3\ q + 2\ q^{2} + q^{3}$

$F_{4} = 5\ q + 5\ q^{2} + 2\ q^{3} + q^{4}$

$F_{5} = 7\ q + 9\ q^{2} + 5\ q^{3} + 2\ q^{4} + q^{5}$

$F_{6} = 11\ q + 18\ q^{2} + 11\ q^{3} + 5\ q^{4} + 2\ q^{5} + q^{6}$

$F_{7} = 15\ q + 30\ q^{2} + 22\ q^{3} + 11\ q^{4} + 5\ q^{5} + 2\ q^{6} + q^{7}$

$F_{8} = 22\ q + 53\ q^{2} + 42\ q^{3} + 24\ q^{4} + 11\ q^{5} + 5\ q^{6} + 2\ q^{7} + q^{8}$

$F_{9} = 30\ q + 85\ q^{2} + 78\ q^{3} + 46\ q^{4} + 24\ q^{5} + 11\ q^{6} + 5\ q^{7} + 2\ q^{8} + q^{9}$

$F_{10} = 42\ q + 139\ q^{2} + 138\ q^{3} + 90\ q^{4} + 48\ q^{5} + 24\ q^{6} + 11\ q^{7} + 5\ q^{8} + 2\ q^{9} + q^{10}$

Description

Number of columns of a plane partition.

Map

transpose

Description

The transpose of a plane partition.
This is the mirror symmetry along the vertical axis.