Processing math: 100%

Identifier
Values
[1,0] => [2,1] => 1
[1,0,1,0] => [3,1,2] => 1
[1,1,0,0] => [2,3,1] => 1
[1,0,1,0,1,0] => [4,1,2,3] => 1
[1,0,1,1,0,0] => [3,1,4,2] => 1
[1,1,0,0,1,0] => [2,4,1,3] => 1
[1,1,0,1,0,0] => [4,3,1,2] => 1
[1,1,1,0,0,0] => [2,3,4,1] => 1
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 1
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 1
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 1
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 1
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 1
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 1
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 1
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 1
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 1
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 1
[] => [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 decomposition (or block) number of a permutation.
For π∈Sn, this is given by
#{1≤k≤n:{π1,…,πk}={1,…,k}}.
This is also known as the number of connected components [1] or the number of blocks [2] of the permutation, considering it as a direct sum.
This is one plus St000234The number of global ascents of a permutation..
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.