Identifier
Values
[1,0] => [1] => [1] => 1
[1,0,1,0] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => 2
[1,0,1,0,1,0] => [2,3,1] => [2,3,1] => 1
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => 2
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [2,3,4,1] => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [2,3,1,4] => 2
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [2,4,1,3] => 1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,3,4,2] => 2
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => 3
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [3,1,4,2] => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [3,4,1,2] => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,2,4] => 2
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => 2
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,3,4,5,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,3,4,2,5] => 3
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,3,5,2,4] => 2
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,4,5,3] => 3
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,4,2,5,3] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => 5
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 size of the connectivity set of a signed permutation.
According to [1], the connectivity set of a signed permutation $w\in\mathfrak H_n$ is $n$ minus the number of generators appearing in any reduced word for $w$.
The connectivity set can be defined for arbitrary Coxeter systems. For permutations, see St000234The number of global ascents of a permutation.. For the number of connected elements in a Coxeter system see St001888The number of connected elements in the Coxeter group corresponding to a finite Cartan type..
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.