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Identifier

St001599: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 1

[1,1] => 1

[3] => 2

[2,1] => 3

[1,1,1] => 1

[4] => 4

[3,1] => 9

[2,2] => 5

[2,1,1] => 7

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

[5] => 9

[4,1] => 26

[3,2] => 28

[3,1,1] => 30

[2,2,1] => 24

[2,1,1,1] => 17

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

[6] => 20

[5,1] => 75

[4,2] => 114

[4,1,1] => 117

[3,3] => 59

[3,2,1] => 170

[3,1,1,1] => 96

[2,2,2] => 49

[2,2,1,1] => 83

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

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

[7] => 48

[6,1] => 214

[5,2] => 421

[5,1,1] => 419

[4,3] => 382

[4,2,1] => 874

[4,1,1,1] => 459

[3,3,1] => 493

[3,2,2] => 474

[3,2,1,1] => 745

[3,1,1,1,1] => 294

[2,2,2,1] => 281

[2,2,1,1,1] => 261

[2,1,1,1,1,1] => 104

[1,1,1,1,1,1,1] => 16

[8] => 115

[7,1] => 612

[6,2] => 1462

[6,1,1] => 1446

[5,3] => 1833

[5,2,1] => 3875

[5,1,1,1] => 1966

[4,4] => 868

[4,3,1] => 3930

[4,2,2] => 3014

[4,2,1,1] => 4619

[4,1,1,1,1] => 1657

[3,3,2] => 2154

[3,3,1,1] => 2742

[3,2,2,1] => 3309

[3,2,1,1,1] => 2847

[3,1,1,1,1,1] => 863

[2,2,2,2] => 615

[2,2,2,1,1] => 1181

[2,2,1,1,1,1] => 789

[2,1,1,1,1,1,1] => 257

[1,1,1,1,1,1,1,1] => 34

[9] => 286

[8,1] => 1747

[7,2] => 4918

[7,1,1] => 4834

[6,3] => 7733

[6,2,1] => 15795

[6,1,1,1] => 7881

[5,4] => 6309

[5,3,1] => 22276

[5,2,2] => 15880

[5,2,1,1] => 23968

[5,1,1,1,1] => 8243

[4,4,1] => 11068

[4,3,2] => 20851

[4,3,1,1] => 25758

[4,2,2,1] => 24878

[4,2,1,1,1] => 20609

[4,1,1,1,1,1] => 5646

[3,3,3] => 4901

[3,3,2,1] => 18597

[3,3,1,1,1] => 12607

[3,2,2,2] => 8857

[3,2,2,1,1] => 16474

[3,2,1,1,1,1] => 10041

[3,1,1,1,1,1,1] => 2473

[2,2,2,2,1] => 4016

[2,2,2,1,1,1] => 4378

[2,2,1,1,1,1,1] => 2313

[2,1,1,1,1,1,1,1] => 637

[1,1,1,1,1,1,1,1,1] => 75

[10] => 719

[9,1] => 4995

[8,2] => 16146

[8,1,1] => 15857

[7,3] => 30362

>>> Load all 746 entries. <<<

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Description

The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees.

Code

def statistic(mu):
    s = SymmetricFunctions(QQ).s()
    A = CombinatorialSpecies()
    X = species.SingletonSpecies()
    E = species.SetSpecies()
    A.define(X*E(A))
    F = A.cycle_index_series()
    return F.coefficient(mu.size()).scalar(s(mu))

Created

Sep 26, 2020 at 23:49 by Martin Rubey

Updated

Sep 26, 2020 at 23:49 by Martin Rubey