Identifier
Values
[1] => [1,0] => 2
[1,1] => [1,0,1,0] => 3
[2] => [1,1,0,0] => 2
[1,1,1] => [1,0,1,0,1,0] => 4
[1,2] => [1,0,1,1,0,0] => 3
[2,1] => [1,1,0,0,1,0] => 2
[3] => [1,1,1,0,0,0] => 2
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 5
[1,1,2] => [1,0,1,0,1,1,0,0] => 4
[1,2,1] => [1,0,1,1,0,0,1,0] => 3
[1,3] => [1,0,1,1,1,0,0,0] => 3
[2,1,1] => [1,1,0,0,1,0,1,0] => 3
[2,2] => [1,1,0,0,1,1,0,0] => 2
[3,1] => [1,1,1,0,0,0,1,0] => 2
[4] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 3
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 4
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5] => [1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
>>> Load all 127 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. Then we calculate the global dimension of that CNakayama algebra.
Map
bounce path
Description
The bounce path determined by an integer composition.