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Identifier

St001643: Dyck paths ⟶ ℤ

Values

[1,0] => 1

[1,0,1,0] => 3

[1,1,0,0] => 1

[1,0,1,0,1,0] => 5

[1,0,1,1,0,0] => 4

[1,1,0,0,1,0] => 4

[1,1,0,1,0,0] => 3

[1,1,1,0,0,0] => 1

[1,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,1,0,0] => 6

[1,0,1,1,0,0,1,0] => 7

[1,0,1,1,0,1,0,0] => 6

[1,0,1,1,1,0,0,0] => 5

[1,1,0,0,1,0,1,0] => 6

[1,1,0,0,1,1,0,0] => 6

[1,1,0,1,0,0,1,0] => 6

[1,1,0,1,0,1,0,0] => 6

[1,1,0,1,1,0,0,0] => 4

[1,1,1,0,0,0,1,0] => 5

[1,1,1,0,0,1,0,0] => 4

[1,1,1,0,1,0,0,0] => 3

[1,1,1,1,0,0,0,0] => 1

[1,0,1,0,1,0,1,0,1,0] => 9

[1,0,1,0,1,0,1,1,0,0] => 8

[1,0,1,0,1,1,0,0,1,0] => 9

[1,0,1,0,1,1,0,1,0,0] => 8

[1,0,1,0,1,1,1,0,0,0] => 7

[1,0,1,1,0,0,1,0,1,0] => 9

[1,0,1,1,0,0,1,1,0,0] => 9

[1,0,1,1,0,1,0,0,1,0] => 9

[1,0,1,1,0,1,0,1,0,0] => 9

[1,0,1,1,0,1,1,0,0,0] => 7

[1,0,1,1,1,0,0,0,1,0] => 9

[1,0,1,1,1,0,0,1,0,0] => 8

[1,0,1,1,1,0,1,0,0,0] => 7

[1,0,1,1,1,1,0,0,0,0] => 6

[1,1,0,0,1,0,1,0,1,0] => 8

[1,1,0,0,1,0,1,1,0,0] => 7

[1,1,0,0,1,1,0,0,1,0] => 9

[1,1,0,0,1,1,0,1,0,0] => 8

[1,1,0,0,1,1,1,0,0,0] => 8

[1,1,0,1,0,0,1,0,1,0] => 8

[1,1,0,1,0,0,1,1,0,0] => 8

[1,1,0,1,0,1,0,0,1,0] => 9

[1,1,0,1,0,1,0,1,0,0] => 9

[1,1,0,1,0,1,1,0,0,0] => 8

[1,1,0,1,1,0,0,0,1,0] => 8

[1,1,0,1,1,0,0,1,0,0] => 7

[1,1,0,1,1,0,1,0,0,0] => 7

[1,1,0,1,1,1,0,0,0,0] => 5

[1,1,1,0,0,0,1,0,1,0] => 7

[1,1,1,0,0,0,1,1,0,0] => 8

[1,1,1,0,0,1,0,0,1,0] => 7

[1,1,1,0,0,1,0,1,0,0] => 8

[1,1,1,0,0,1,1,0,0,0] => 6

[1,1,1,0,1,0,0,0,1,0] => 7

[1,1,1,0,1,0,0,1,0,0] => 7

[1,1,1,0,1,0,1,0,0,0] => 6

[1,1,1,0,1,1,0,0,0,0] => 4

[1,1,1,1,0,0,0,0,1,0] => 6

[1,1,1,1,0,0,0,1,0,0] => 5

[1,1,1,1,0,0,1,0,0,0] => 4

[1,1,1,1,0,1,0,0,0,0] => 3

[1,1,1,1,1,0,0,0,0,0] => 1

[1,0,1,0,1,0,1,0,1,0,1,0] => 11

[1,0,1,0,1,0,1,0,1,1,0,0] => 10

[1,0,1,0,1,0,1,1,0,0,1,0] => 11

[1,0,1,0,1,0,1,1,0,1,0,0] => 10

[1,0,1,0,1,0,1,1,1,0,0,0] => 9

[1,0,1,0,1,1,0,0,1,0,1,0] => 11

[1,0,1,0,1,1,0,0,1,1,0,0] => 11

[1,0,1,0,1,1,0,1,0,0,1,0] => 11

[1,0,1,0,1,1,0,1,0,1,0,0] => 11

[1,0,1,0,1,1,0,1,1,0,0,0] => 9

[1,0,1,0,1,1,1,0,0,0,1,0] => 11

[1,0,1,0,1,1,1,0,0,1,0,0] => 10

[1,0,1,0,1,1,1,0,1,0,0,0] => 9

[1,0,1,0,1,1,1,1,0,0,0,0] => 8

[1,0,1,1,0,0,1,0,1,0,1,0] => 11

[1,0,1,1,0,0,1,0,1,1,0,0] => 10

[1,0,1,1,0,0,1,1,0,0,1,0] => 12

[1,0,1,1,0,0,1,1,0,1,0,0] => 11

[1,0,1,1,0,0,1,1,1,0,0,0] => 11

[1,0,1,1,0,1,0,0,1,0,1,0] => 11

[1,0,1,1,0,1,0,0,1,1,0,0] => 11

[1,0,1,1,0,1,0,1,0,0,1,0] => 12

[1,0,1,1,0,1,0,1,0,1,0,0] => 12

[1,0,1,1,0,1,0,1,1,0,0,0] => 11

[1,0,1,1,0,1,1,0,0,0,1,0] => 11

[1,0,1,1,0,1,1,0,0,1,0,0] => 10

[1,0,1,1,0,1,1,0,1,0,0,0] => 10

[1,0,1,1,0,1,1,1,0,0,0,0] => 8

[1,0,1,1,1,0,0,0,1,0,1,0] => 11

[1,0,1,1,1,0,0,0,1,1,0,0] => 12

[1,0,1,1,1,0,0,1,0,0,1,0] => 11

[1,0,1,1,1,0,0,1,0,1,0,0] => 12

[1,0,1,1,1,0,0,1,1,0,0,0] => 10

[1,0,1,1,1,0,1,0,0,0,1,0] => 11

[1,0,1,1,1,0,1,0,0,1,0,0] => 11

[1,0,1,1,1,0,1,0,1,0,0,0] => 10

[1,0,1,1,1,0,1,1,0,0,0,0] => 8

>>> Load all 655 entries. <<<

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Description

The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path.

References

[1] Artenstein, D., González, A., Mata, G. Nearly Frobenius dimension on Frobenius algebras arXiv:2011.09790

Code

gap('LoadPackage("QPA");')

def kupisch(D):
    H = D.heights()
    return [1+H[i] for i, s in enumerate(D) if s == 0]+[1]

def statistic(D):
    D = DyckWord(D)
    K = kupisch(D)
    A = gap.NakayamaAlgebra(K, gap.GF(3))
    injA = gap.IndecInjectiveModules(A)
    projA = gap.IndecProjectiveModules(A)
    CoRegA = gap.DirectSumOfQPAModules(injA)
    RegA = gap.DirectSumOfQPAModules(projA)
    return gap.Size(gap.HomOverAlgebra(CoRegA, RegA))

Created

Nov 20, 2020 at 09:14 by Rene Marczinzik

Updated

Nov 20, 2020 at 12:53 by Martin Rubey