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Identifier
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.
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