Identifier
Values
[1,0] => [1,1,0,0] => 1100 => 1001 => 1
[1,0,1,0] => [1,1,0,1,0,0] => 110100 => 100001 => 1
[1,1,0,0] => [1,1,1,0,0,0] => 111000 => 101101 => 1
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 11010100 => 10000001 => 1
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 11011000 => 10001101 => 1
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 11100100 => 10110001 => 2
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 11101000 => 10111101 => 1
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 11110000 => 10100101 => 2
[] => [1,0] => 10 => 11 => 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
Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.