Identifier
Values
[1] => [1,0,1,0] => [1,1,0,0] => 6
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,0] => 10
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 9
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0] => 14
[2,1] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 8
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 12
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 18
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0] => 12
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0] => 15
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 11
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 14
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 21
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 16
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => 13
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0] => 10
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 13
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 12
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 15
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 17
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 17
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0] => 21
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 11
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 12
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 20
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 16
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 14
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 19
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 17
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 19
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 15
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 11
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 19
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 18
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 14
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 13
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 18
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 18
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 23
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 19
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 15
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 27
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 17
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 16
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 13
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 13
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 17
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 17
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 15
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 15
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 25
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 21
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 25
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 21
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 19
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 17
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 12
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 25
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 15
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 14
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 15
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 28
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 13
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 19
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 23
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 16
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 23
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 22
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 17
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 18
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 14
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 23
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 23
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 26
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 12
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 18
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 21
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 16
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 26
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 22
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 16
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 17
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 18
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 21
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 24
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 16
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 17
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 18
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 15
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 24
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 21
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 19
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 24
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 20
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 15
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 16
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 24
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 24
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 18
>>> Load all 131 entries. <<<
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 20
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 17
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 19
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 22
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 16
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 14
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 15
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 22
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 17
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 22
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 22
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 16
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 20
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 19
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 16
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 16
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 20
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 20
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 15
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 20
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 16
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 15
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 19
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 18
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 16
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 14
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 18
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 16
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 15
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
The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.