Identifier
- St001531: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[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
[1,0,1,1,1,1,0,0,0,1,0,0]=>80
[1,0,1,1,1,1,0,0,1,0,0,0]=>145
[1,0,1,1,1,1,0,1,0,0,0,0]=>238
[1,0,1,1,1,1,1,0,0,0,0,0]=>357
[1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,0]=>14
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,0]=>16
[1,1,0,0,1,1,0,1,1,0,0,0]=>28
[1,1,0,0,1,1,1,0,0,0,1,0]=>14
[1,1,0,0,1,1,1,0,0,1,0,0]=>28
[1,1,0,0,1,1,1,0,1,0,0,0]=>50
[1,1,0,0,1,1,1,1,0,0,0,0]=>80
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,1,0,0,0]=>28
[1,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,0]=>16
[1,1,0,1,0,1,0,1,0,0,1,0]=>16
[1,1,0,1,0,1,0,1,0,1,0,0]=>32
[1,1,0,1,0,1,0,1,1,0,0,0]=>56
[1,1,0,1,0,1,1,0,0,0,1,0]=>28
[1,1,0,1,0,1,1,0,0,1,0,0]=>56
[1,1,0,1,0,1,1,0,1,0,0,0]=>100
[1,1,0,1,0,1,1,1,0,0,0,0]=>160
[1,1,0,1,1,0,0,0,1,0,1,0]=>14
[1,1,0,1,1,0,0,0,1,1,0,0]=>28
[1,1,0,1,1,0,0,1,0,0,1,0]=>28
[1,1,0,1,1,0,0,1,0,1,0,0]=>56
[1,1,0,1,1,0,0,1,1,0,0,0]=>98
[1,1,0,1,1,0,1,0,0,0,1,0]=>50
[1,1,0,1,1,0,1,0,0,1,0,0]=>100
[1,1,0,1,1,0,1,0,1,0,0,0]=>178
[1,1,0,1,1,0,1,1,0,0,0,0]=>290
[1,1,0,1,1,1,0,0,0,0,1,0]=>80
[1,1,0,1,1,1,0,0,0,1,0,0]=>160
[1,1,0,1,1,1,0,0,1,0,0,0]=>290
[1,1,0,1,1,1,0,1,0,0,0,0]=>476
[1,1,0,1,1,1,1,0,0,0,0,0]=>714
[1,1,1,0,0,0,1,0,1,0,1,0]=>7
[1,1,1,0,0,0,1,0,1,1,0,0]=>14
[1,1,1,0,0,0,1,1,0,0,1,0]=>14
[1,1,1,0,0,0,1,1,0,1,0,0]=>28
[1,1,1,0,0,0,1,1,1,0,0,0]=>49
[1,1,1,0,0,1,0,0,1,0,1,0]=>14
[1,1,1,0,0,1,0,0,1,1,0,0]=>28
[1,1,1,0,0,1,0,1,0,0,1,0]=>28
[1,1,1,0,0,1,0,1,0,1,0,0]=>56
[1,1,1,0,0,1,0,1,1,0,0,0]=>98
[1,1,1,0,0,1,1,0,0,0,1,0]=>49
[1,1,1,0,0,1,1,0,0,1,0,0]=>98
[1,1,1,0,0,1,1,0,1,0,0,0]=>175
[1,1,1,0,0,1,1,1,0,0,0,0]=>280
[1,1,1,0,1,0,0,0,1,0,1,0]=>25
[1,1,1,0,1,0,0,0,1,1,0,0]=>50
[1,1,1,0,1,0,0,1,0,0,1,0]=>50
[1,1,1,0,1,0,0,1,0,1,0,0]=>100
[1,1,1,0,1,0,0,1,1,0,0,0]=>175
[1,1,1,0,1,0,1,0,0,0,1,0]=>89
[1,1,1,0,1,0,1,0,0,1,0,0]=>178
[1,1,1,0,1,0,1,0,1,0,0,0]=>317
[1,1,1,0,1,0,1,1,0,0,0,0]=>515
[1,1,1,0,1,1,0,0,0,0,1,0]=>145
[1,1,1,0,1,1,0,0,0,1,0,0]=>290
[1,1,1,0,1,1,0,0,1,0,0,0]=>526
[1,1,1,0,1,1,0,1,0,0,0,0]=>859
[1,1,1,0,1,1,1,0,0,0,0,0]=>1309
[1,1,1,1,0,0,0,0,1,0,1,0]=>40
[1,1,1,1,0,0,0,0,1,1,0,0]=>80
[1,1,1,1,0,0,0,1,0,0,1,0]=>80
[1,1,1,1,0,0,0,1,0,1,0,0]=>160
[1,1,1,1,0,0,0,1,1,0,0,0]=>280
[1,1,1,1,0,0,1,0,0,0,1,0]=>145
[1,1,1,1,0,0,1,0,0,1,0,0]=>290
[1,1,1,1,0,0,1,0,1,0,0,0]=>515
[1,1,1,1,0,0,1,1,0,0,0,0]=>850
[1,1,1,1,0,1,0,0,0,0,1,0]=>238
[1,1,1,1,0,1,0,0,0,1,0,0]=>476
[1,1,1,1,0,1,0,0,1,0,0,0]=>859
[1,1,1,1,0,1,0,1,0,0,0,0]=>1427
[1,1,1,1,0,1,1,0,0,0,0,0]=>2194
[1,1,1,1,1,0,0,0,0,0,1,0]=>357
[1,1,1,1,1,0,0,0,0,1,0,0]=>714
[1,1,1,1,1,0,0,0,1,0,0,0]=>1309
[1,1,1,1,1,0,0,1,0,0,0,0]=>2194
[1,1,1,1,1,0,1,0,0,0,0,0]=>3377
[1,1,1,1,1,1,0,0,0,0,0,0]=>4824
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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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