Identifier
Values
[1] => [1,0,1,0] => [1,1,0,0] => 1100 => 2
[2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 101100 => 2
[1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 110010 => 2
[3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 11011000 => 2
[2,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 111000 => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 11100100 => 2
[3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => 10101100 => 2
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 10110010 => 4
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 11001010 => 2
[3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 10111000 => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 11001100 => 4
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 11100010 => 3
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 11110000 => 4
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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.