- FindStat

Identifier

Mp00284: Standard tableaux —rows⟶ Set partitions
St000505: Set partitions ⟶ ℤ

Values

[[1]] => {{1}} => 1

[[1,2]] => {{1,2}} => 2

[[1],[2]] => {{1},{2}} => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = q$

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

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

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

$F_{5} = q + 3\ q^{2} + 5\ q^{3} + 7\ q^{4} + 10\ q^{5}$

$F_{6} = q + 6\ q^{2} + 10\ q^{3} + 14\ q^{4} + 19\ q^{5} + 26\ q^{6}$

$F_{7} = q + 10\ q^{2} + 19\ q^{3} + 29\ q^{4} + 41\ q^{5} + 56\ q^{6} + 76\ q^{7}$

Description

The biggest entry in the block containing the 1.

Map

rows

Description

The set partition whose blocks are the rows of the tableau.