searching the database
Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000329
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000329: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000329: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,2,3] => [1,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,3,2] => [2,1]
=> [1]
=> [1,0,1,0]
=> 0
[2,1,3] => [2,1]
=> [1]
=> [1,0,1,0]
=> 0
[3,2,1] => [2,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,2,4,3] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,3,2,4] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,3,4,2] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,4,2,3] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,4,3,2] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[2,1,3,4] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[2,1,4,3] => [2,2]
=> [2]
=> [1,1,0,0,1,0]
=> 1
[2,3,1,4] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[2,4,3,1] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[3,1,2,4] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[3,2,1,4] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[3,2,4,1] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[3,4,1,2] => [2,2]
=> [2]
=> [1,1,0,0,1,0]
=> 1
[4,1,3,2] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[4,2,1,3] => [3,1]
=> [1]
=> [1,0,1,0]
=> 0
[4,2,3,1] => [2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[4,3,2,1] => [2,2]
=> [2]
=> [1,1,0,0,1,0]
=> 1
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,2,4,5,3] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,2,5,3,4] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,2,5,4,3] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,3,2,5,4] => [2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> 0
[1,3,4,2,5] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,3,4,5,2] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,3,5,2,4] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,3,5,4,2] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,4,2,3,5] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,4,2,5,3] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,4,3,2,5] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,4,3,5,2] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,4,5,2,3] => [2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> 0
[1,4,5,3,2] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,5,2,3,4] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,5,2,4,3] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,5,3,2,4] => [3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> 1
[1,5,3,4,2] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,5,4,2,3] => [4,1]
=> [1]
=> [1,0,1,0]
=> 0
[1,5,4,3,2] => [2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> 0
[2,1,3,4,5] => [2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 1
[2,1,3,5,4] => [2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> 0
[2,1,4,3,5] => [2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> 0
Description
The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1.
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!