Identifier
-
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
St001295: Dyck paths ⟶ ℤ (values match St000012The area of a Dyck path.)
Values
[1] => [1,0] => 0
[1,1] => [1,0,1,0] => 0
[2] => [1,1,0,0] => 1
[1,1,1] => [1,0,1,0,1,0] => 0
[1,2] => [1,0,1,1,0,0] => 1
[2,1] => [1,1,0,0,1,0] => 1
[3] => [1,1,1,0,0,0] => 3
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,3] => [1,0,1,1,1,0,0,0] => 3
[2,1,1] => [1,1,0,0,1,0,1,0] => 1
[2,2] => [1,1,0,0,1,1,0,0] => 2
[3,1] => [1,1,1,0,0,0,1,0] => 3
[4] => [1,1,1,1,0,0,0,0] => 6
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 6
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 4
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 4
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 6
[5] => [1,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[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] => 1
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[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] => 10
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 4
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
[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] => 7
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 10
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 15
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
Gives the vector space dimension of the homomorphism space between J^2 and J^2.
Map
bounce path
Description
The bounce path determined by an integer composition.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!