Identifier
Values
{{1}} => [1] => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => [2,1] => 0
{{1},{2}} => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [2,3,1] => [2,3,1] => 0
{{1,2},{3}} => [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}} => [3,2,1] => [3,2,1] => [3,2,1] => 0
{{1},{2,3}} => [1,3,2] => [3,1,2] => [3,1,2] => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => [2,3,4,1] => 0
{{1,2,3},{4}} => [2,3,1,4] => [2,3,1,4] => [2,3,1,4] => 0
{{1,2,4},{3}} => [2,4,3,1] => [4,2,3,1] => [4,2,3,1] => 0
{{1,2},{3,4}} => [2,1,4,3] => [2,4,1,3] => [2,4,1,3] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => [3,2,4,1] => 0
{{1,3},{2,4}} => [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => [3,4,1,2] => [3,4,1,2] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [2,4,3,1] => [2,4,3,1] => 0
{{1},{2,4},{3}} => [1,4,3,2] => [4,3,1,2] => [4,3,1,2] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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 number of alignments of type EN of a signed permutation.
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
  • $-i < 0 < -\pi(i) < \pi(j) < j$
  • $i \leq\pi(i) < \pi(j) < j$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
Map
to signed permutation
Description
The signed permutation with all signs positive.