Identifier
Values
[1] => [1,0] => [1,0] => 0
[1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
[2,1] => [1,1,0,0,1,0] => [1,1,1,0,0,0] => 0
[3] => [1,1,1,0,0,0] => [1,0,1,1,0,0] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 2
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
[1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 0
[2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 0
[3,1] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[4] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 3
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 4
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
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Description
The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra.
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Map
bounce path
Description
The bounce path determined by an integer composition.