Identifier
- St001531: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => 1
[1,1,0,0] => 2
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 4
[1,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0] => 14
[1,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,0] => 25
[1,1,1,1,0,0,0,0] => 40
[1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,0,0] => 25
[1,0,1,1,1,1,0,0,0,0] => 40
[1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,0] => 14
[1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,0,0] => 28
[1,1,0,1,1,0,0,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,0] => 28
[1,1,0,1,1,0,1,0,0,0] => 50
[1,1,0,1,1,1,0,0,0,0] => 80
[1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,1,0,0] => 14
[1,1,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,1,0,0] => 28
[1,1,1,0,0,1,1,0,0,0] => 49
[1,1,1,0,1,0,0,0,1,0] => 25
[1,1,1,0,1,0,0,1,0,0] => 50
[1,1,1,0,1,0,1,0,0,0] => 89
[1,1,1,0,1,1,0,0,0,0] => 145
[1,1,1,1,0,0,0,0,1,0] => 40
[1,1,1,1,0,0,0,1,0,0] => 80
[1,1,1,1,0,0,1,0,0,0] => 145
[1,1,1,1,0,1,0,0,0,0] => 238
[1,1,1,1,1,0,0,0,0,0] => 357
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,0,1,1,1,0,1,0,0,0] => 25
[1,0,1,0,1,1,1,1,0,0,0,0] => 40
[1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,1,1,0,0,0] => 28
[1,0,1,1,0,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,1,0,0] => 28
[1,0,1,1,0,1,1,0,1,0,0,0] => 50
[1,0,1,1,0,1,1,1,0,0,0,0] => 80
[1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,0,1,0] => 14
[1,0,1,1,1,0,0,1,0,1,0,0] => 28
[1,0,1,1,1,0,0,1,1,0,0,0] => 49
[1,0,1,1,1,0,1,0,0,0,1,0] => 25
[1,0,1,1,1,0,1,0,0,1,0,0] => 50
[1,0,1,1,1,0,1,0,1,0,0,0] => 89
[1,0,1,1,1,0,1,1,0,0,0,0] => 145
[1,0,1,1,1,1,0,0,0,0,1,0] => 40
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Description
Number of partial orders contained in the poset determined by the Dyck path.
A Dyck path determines a poset, where the relations correspond to boxes under the path (seen as a North-East path). This statistic is closely related to unicellular LLT polynomials and their e-expansion.
A Dyck path determines a poset, where the relations correspond to boxes under the path (seen as a North-East path). This statistic is closely related to unicellular LLT polynomials and their e-expansion.
References
[1] Alexandersson, P., Sulzgruber, R. A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions arXiv:2004.09198
Created
Apr 21, 2020 at 11:21 by Per Alexandersson
Updated
Apr 21, 2020 at 11:21 by Per Alexandersson
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