Identifier
Values
[1,0] => 10 => [1,1] => [1,0,1,0] => 2
[1,0,1,0] => 1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0] => 1100 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0] => 101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0] => 101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0] => 110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0] => 110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0] => 111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
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Description
The finitistic dominant dimension of a Dyck path.
To every LNakayama algebra there is a corresponding Dyck path, see also St000684The global dimension of the LNakayama algebra associated to a Dyck path.. We associate the finitistic dominant dimension of the algebra to the corresponding Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.