Identifier
Values
01 => [1,1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
10 => [1,1] => [1,0,1,0] => [1,1,0,1,0,0] => 2
001 => [2,1] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
010 => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
011 => [1,2] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
100 => [1,2] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
101 => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
110 => [2,1] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
0001 => [3,1] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
0011 => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
0111 => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
1000 => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
1100 => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
1110 => [3,1] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
bounce path
Description
The bounce path determined by an integer composition.
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 $w$.