Identifier
Values
[1,0] => [2,1] => [2,1] => 1
[1,0,1,0] => [3,1,2] => [3,1,2] => 1
[1,1,0,0] => [2,3,1] => [3,2,1] => 1
[1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => 1
[1,0,1,1,0,0] => [3,1,4,2] => [4,3,1,2] => 1
[1,1,0,0,1,0] => [2,4,1,3] => [4,2,1,3] => 1
[1,1,0,1,0,0] => [4,3,1,2] => [3,1,4,2] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [4,3,2,1] => 1
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,1,2,3,4] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,4,1,2,3] => 1
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,3,1,2,4] => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,1,2,5,3] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,4,3,1,2] => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,4,2,1,3] => 1
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,5,2,4] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,1,5,2,3] => 2
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,1,5,4,2] => 1
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,3,2,1,4] => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,2,1,5,3] => 1
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,3,1,5,2] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,5,1,2,3,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,4,1,2,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [5,1,2,3,6,4] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,5,4,1,2,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,3,1,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,5,3,1,2,4] => 1
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [4,1,2,6,3,5] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,1,2,6,3,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,1,2,6,5,3] => 1
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,4,3,1,2,5] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,3,1,2,6,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,4,1,2,6,3] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,5,4,3,1,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,5,2,1,3,4] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,4,2,1,3,5] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [5,2,1,3,6,4] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,5,4,2,1,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,1,6,5,2,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,1,6,2,3,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,1,5,2,3,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,1,6,5,2,3] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,1,6,4,2,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,1,5,2,6,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,4,1,6,2,3] => 2
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,1,6,5,4,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,3,2,1,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,5,3,2,1,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,2,1,6,3,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,2,1,6,3,4] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,2,1,6,5,3] => 1
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,3,1,6,2,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,3,1,6,2,4] => 2
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,1,5,2,6,3] => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,3,1,6,5,2] => 1
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,4,3,2,1,5] => 1
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,3,2,1,6,4] => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,4,2,1,6,3] => 1
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,4,3,1,6,2] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,6,1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,5,1,2,3,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [6,1,2,3,4,7,5] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,6,5,1,2,3,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,4,1,2,3,5,6] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [5,1,2,3,7,4,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [6,1,2,3,7,4,5] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,6,5,4,1,2,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,3,1,2,4,5,6] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,6,5,4,3,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,4,2,1,3,5,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [7,3,2,1,4,5,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,6,5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,7,1,2,3,4,5,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [7,1,2,3,4,5,8,6] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,7,6,1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [7,1,2,3,4,8,5,6] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,7,6,5,1,2,3,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,4,1,2,3,5,6,7] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,7,6,5,4,1,2,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,3,1,2,4,5,6,7] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [5,1,2,8,3,4,6,7] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,6,5,4,3,1,2,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,7,6,5,4,3,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,6,4,2,1,3,5,7] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,7,6,4,2,1,3,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [8,6,5,4,2,1,3,7] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,7,6,5,4,2,1,3] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [6,1,8,2,3,4,5,7] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [3,1,5,2,7,4,8,6] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [3,1,6,2,7,4,8,5] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [8,3,2,1,4,5,6,7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [4,1,5,2,7,3,8,6] => 2
>>> Load all 107 entries. <<<
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,6,4,3,2,1,5,7] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,7,6,4,3,2,1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [8,6,5,4,3,2,1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,7,6,5,4,3,2,1] => 1
[] => [1] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,9,8,7,6,5,4,3,2,1] => 1
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Description
The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation.
These are multiplicities of Verma modules.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].