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Identifier

St001780: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 1

[1,1] => 1

[3] => 1

[2,1] => 2

[1,1,1] => 1

[4] => 1

[3,1] => 3

[2,2] => 2

[2,1,1] => 3

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

[5] => 1

[4,1] => 4

[3,2] => 6

[3,1,1] => 4

[2,2,1] => 6

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

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

[6] => 1

[5,1] => 5

[4,2] => 20

[4,1,1] => 5

[3,3] => 6

[3,2,1] => 12

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

[2,2,2] => 6

[2,2,1,1] => 20

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

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

[7] => 1

[6,1] => 6

[5,2] => 30

[5,1,1] => 6

[4,3] => 8

[4,2,1] => 260

[4,1,1,1] => 6

[3,3,1] => 195

[3,2,2] => 195

[3,2,1,1] => 260

[3,1,1,1,1] => 6

[2,2,2,1] => 8

[2,2,1,1,1] => 30

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

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

[8] => 1

[7,1] => 7

[6,2] => 42

[6,1,1] => 7

[5,3] => 560

[5,2,1] => 924

[5,1,1,1] => 7

[4,4] => 8

[4,3,1] => 352

[4,2,2] => 462

[4,2,1,1] => 660

[4,1,1,1,1] => 7

[3,3,2] => 9

[3,3,1,1] => 462

[3,2,2,1] => 352

[3,2,1,1,1] => 924

[3,1,1,1,1,1] => 7

[2,2,2,2] => 8

[2,2,2,1,1] => 560

[2,2,1,1,1,1] => 42

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

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

[9] => 1

[8,1] => 8

[7,2] => 56

[7,1,1] => 8

[6,3] => 312

[6,2,1] => 3696

[6,1,1,1] => 8

[5,4] => 10

[5,3,1] => 26400

[5,2,2] => 1848

[5,2,1,1] => 308154

[5,1,1,1,1] => 8

[4,4,1] => 6188

[4,3,2] => 252

[4,3,1,1] => 32760

[4,2,2,1] => 32760

[4,2,1,1,1] => 308154

[4,1,1,1,1,1] => 8

[3,3,3] => 9

[3,3,2,1] => 252

[3,3,1,1,1] => 1848

[3,2,2,2] => 6188

[3,2,2,1,1] => 26400

[3,2,1,1,1,1] => 3696

[3,1,1,1,1,1,1] => 8

[2,2,2,2,1] => 10

[2,2,2,1,1,1] => 312

[2,2,1,1,1,1,1] => 56

[2,1,1,1,1,1,1,1] => 8

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

[10] => 1

[9,1] => 9

[8,2] => 72

[8,1,1] => 9

[7,3] => 2394

>>> Load all 382 entries. <<<

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Description

The order of promotion on the set of standard tableaux of given shape.

References

[1] Stanley, R. P. Promotion and evacuation MathSciNet:2515772

Code

def statistic(la):
    from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
    return lcm(len(o) for o in orbit_decomposition(StandardTableaux(la), lambda T: T.promotion()))

Created

Mar 23, 2022 at 09:32 by Martin Rubey

Updated

Mar 23, 2022 at 11:22 by Martin Rubey