Identifier
Values
[1] => [1,0] => 0
[1,1] => [1,0,1,0] => 1
[2] => [1,1,0,0] => 0
[1,1,1] => [1,0,1,0,1,0] => 2
[1,2] => [1,0,1,1,0,0] => 1
[2,1] => [1,1,0,0,1,0] => 1
[3] => [1,1,1,0,0,0] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,3] => [1,0,1,1,1,0,0,0] => 1
[2,1,1] => [1,1,0,0,1,0,1,0] => 2
[2,2] => [1,1,0,0,1,1,0,0] => 1
[3,1] => [1,1,1,0,0,0,1,0] => 1
[4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
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Description
The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra.
See http://www.findstat.org/DyckPaths/NakayamaAlgebras.
The number of algebras where the statistic returns a value less than or equal to 1 might be given by the Motzkin numbers oeis.org/A001006.
Map
bounce path
Description
The bounce path determined by an integer composition.