Identifier
Values
[1,0] => [2,1] => 2
[1,0,1,0] => [3,1,2] => 3
[1,1,0,0] => [2,3,1] => 3
[1,0,1,0,1,0] => [4,1,2,3] => 4
[1,0,1,1,0,0] => [3,1,4,2] => 4
[1,1,0,0,1,0] => [2,4,1,3] => 4
[1,1,0,1,0,0] => [4,3,1,2] => 4
[1,1,1,0,0,0] => [2,3,4,1] => 4
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 5
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 5
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 5
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 5
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 5
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 5
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 5
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 5
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 5
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 5
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 5
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 5
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 5
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 5
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 6
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 6
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 6
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 6
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 6
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 6
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 6
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 6
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 6
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 6
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 6
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 6
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 6
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 6
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 6
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 6
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 6
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 6
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 6
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 6
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 6
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => 6
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 6
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 6
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 6
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 6
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 6
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 6
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 6
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 6
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 6
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 6
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 6
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 6
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 6
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 6
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 6
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 6
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 6
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 6
[] => [1] => 1
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
Description
The size of the first part in the decomposition of a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is defined to be the smallest $k > 0$ such that $\{\pi(1),\ldots,\pi(k)\} = \{1,\ldots,k\}$. This statistic is undefined for the empty permutation.
For the number of parts in the decomposition see St000056The decomposition (or block) number of a permutation..
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.