- FindStat

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Identifier

St000816: Integer compositions ⟶ ℤ

Values

[1] => 1

[1,1] => 1

[2] => 1

[1,1,1] => 1

[1,2] => 1

[2,1] => 1

[3] => 1

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

[1,1,2] => 1

[1,2,1] => 1

[1,3] => 2

[2,1,1] => 1

[2,2] => 2

[3,1] => 1

[4] => 1

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

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

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

[1,1,3] => 3

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

[1,2,2] => 2

[1,3,1] => 2

[1,4] => 3

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

[2,1,2] => 1

[2,2,1] => 2

[2,3] => 2

[3,1,1] => 1

[3,2] => 3

[4,1] => 1

[5] => 1

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

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

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

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

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

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

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

[1,1,4] => 6

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

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

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

[1,2,3] => 2

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

[1,3,2] => 5

[1,4,1] => 3

[1,5] => 4

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

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

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

[2,1,3] => 3

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

[2,2,2] => 5

[2,3,1] => 2

[2,4] => 5

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

[3,1,2] => 1

[3,2,1] => 3

[3,3] => 5

[4,1,1] => 1

[4,2] => 4

[5,1] => 1

[6] => 1

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

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

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

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

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

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

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

[1,1,1,4] => 10

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

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

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

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

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

[1,1,3,2] => 7

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

[1,1,5] => 10

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

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

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

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

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

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

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

[1,2,4] => 7

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

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

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

[1,3,3] => 12

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

[1,4,2] => 9

[1,5,1] => 4

[1,6] => 5

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

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

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

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

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

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

>>> Load all 511 entries. <<<

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Description

The number of standard composition tableaux of the composition.
See [1, Def. 4.2.6].
Apparently, the total number of tableaux of given size is the number of involutions.

References

[1] Luoto, K., Mykytiuk, S., van Willigenburg, S. An introduction to quasisymmetric Schur functions MathSciNet:3097867

Code

def statistic(c):
    F = QuasiSymmetricFunctions(ZZ).F()
    QS = QuasiSymmetricFunctions(ZZ).QS()
    return sum(coeff for _, coeff in F(QS(c)))

Created

May 19, 2017 at 23:08 by Martin Rubey

Updated

Nov 19, 2017 at 22:03 by Christian Stump