Identifier
Values
[1] => [1,0] => 1
[1,1] => [1,0,1,0] => 2
[2] => [1,1,0,0] => 2
[1,1,1] => [1,0,1,0,1,0] => 3
[1,2] => [1,0,1,1,0,0] => 3
[2,1] => [1,1,0,0,1,0] => 3
[3] => [1,1,1,0,0,0] => 3
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,2] => [1,0,1,0,1,1,0,0] => 4
[1,2,1] => [1,0,1,1,0,0,1,0] => 4
[1,3] => [1,0,1,1,1,0,0,0] => 4
[2,1,1] => [1,1,0,0,1,0,1,0] => 4
[2,2] => [1,1,0,0,1,1,0,0] => 4
[3,1] => [1,1,1,0,0,0,1,0] => 4
[4] => [1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
[5] => [1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
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 pyramid weight of the Dyck path.
The pyramid weight of a Dyck path is the sum of the lengths of the maximal pyramids (maximal sequences of the form $1^h0^h$) in the path.
Maximal pyramids are called lower interactions by Le Borgne [2], see St000331The number of upper interactions of a Dyck path. and St000335The difference of lower and upper interactions. for related statistics.
Map
bounce path
Description
The bounce path determined by an integer composition.