searching the database
Your data matches 22 different statistics 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: St001777
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St001777: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St001777: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 0
[1,0,1,1,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 0
[1,1,0,0,1,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 1
[1,1,0,1,0,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 0
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 0
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 0
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 0
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 0
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,1,0,0,0]
=> [3] => 0
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 0
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 0
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1] => 2
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 1
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,6] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,5] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,5] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [5] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,6] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,5] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [5] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,4] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,4] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [4] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,5] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,4] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,5] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [5] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,4] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [4] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 0
Description
The number of weak descents in an integer composition.
A weak descent of an integer composition $\alpha=(a_1, \dots, a_n)$ is an index $1\leq i < n$ such that $a_i \geq a_{i+1}$.
Matching statistic: St000899
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St000899: Integer compositions ⟶ ℤResult quality: 90% ●values known / values provided: 93%●distinct values known / distinct values provided: 90%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St000899: Integer compositions ⟶ ℤResult quality: 90% ●values known / values provided: 93%●distinct values known / distinct values provided: 90%
Values
[1,0,1,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 1 = 0 + 1
[1,0,1,1,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 1 = 0 + 1
[1,1,0,0,1,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 2 = 1 + 1
[1,1,0,1,0,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 1 = 0 + 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,1,0,0,0]
=> [3] => 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => 2 = 1 + 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1] => 3 = 2 + 1
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,6] => 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,5] => 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,6] => 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,5] => 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,4] => 3 = 2 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,5] => 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5] => 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => 3 = 2 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [4] => 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [5,5,1,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> [1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [6,3,1,1,1]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> [4,4,1,1,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [4,3,1,1,1,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [4,1,1,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [5,5,4,3,2,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> [5,5,1,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
=> [5,3,1,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [5,1,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
=> [6,6,5,4,3]
=> [1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
=> [10] => ? = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [6,5,4,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
=> [6,4,3,2,1]
=> [1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
=> [6,6,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [6,3,1,1,1]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
=> [6,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
=> [7,3,3,3]
=> [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
=> [7,2,2,2]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
=> [7,3,1,1]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
=> [7,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [10]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1] => ? = 9 + 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
=> [9,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,2] => ? = 7 + 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
=> [8,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,1,3] => ? = 6 + 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
=> [3,1,1,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [2,1,1,1,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
=> [9,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,3] => ? = 6 + 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
=> [8,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [3,2,1,1,1,1,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [2,2,1,1,1,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
=> [8,3,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
=> [8,2,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
=> [3,3,1,1,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
=> [9,4]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
=> [8,3,2]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
=> [9,5]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]
=> [8,3,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
=> [9,6]
=> [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> [2,2,2,2,2,2,1,1,1]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
=> [9,7]
=> [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,8] => ? = 1 + 1
Description
The maximal number of repetitions of an integer composition.
This is the maximal part of the composition obtained by applying the delta morphism.
Matching statistic: St000904
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St000904: Integer compositions ⟶ ℤResult quality: 90% ●values known / values provided: 93%●distinct values known / distinct values provided: 90%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
St000904: Integer compositions ⟶ ℤResult quality: 90% ●values known / values provided: 93%●distinct values known / distinct values provided: 90%
Values
[1,0,1,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 1 = 0 + 1
[1,0,1,1,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 1 = 0 + 1
[1,1,0,0,1,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 2 = 1 + 1
[1,1,0,1,0,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 1 = 0 + 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,1,0,0,0]
=> [3] => 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => 2 = 1 + 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,2] => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2] => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1] => 3 = 2 + 1
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,0,1,0]
=> [1,1] => 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0]
=> [1] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,6] => 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,5] => 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,6] => 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,5] => 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,4] => 3 = 2 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,5] => 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5] => 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,5] => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [5] => 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,4] => 2 = 1 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => 3 = 2 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [3] => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,4] => 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [4] => 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => 2 = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [5,5,1,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> [1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [6,3,1,1,1]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> [4,4,1,1,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [4,3,1,1,1,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [4,1,1,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [5,5,4,3,2,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> [5,5,1,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
=> [5,3,1,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [5,1,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
=> [6,6,5,4,3]
=> [1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
=> [10] => ? = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [6,5,4,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
=> [6,4,3,2,1]
=> [1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
=> [6,6,1,1,1]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [6,3,1,1,1]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
=> [6,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
=> [7,3,3,3]
=> [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
=> [7,2,2,2]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
=> [7,3,1,1]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
=> [7,1,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [10]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1] => ? = 9 + 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
=> [9,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,2] => ? = 7 + 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
=> [8,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,1,3] => ? = 6 + 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
=> [3,1,1,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,8] => ? = 1 + 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> [2,1,1,1,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
=> [9,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,3] => ? = 6 + 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
=> [8,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [3,2,1,1,1,1,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,9] => ? = 0 + 1
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [2,2,1,1,1,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
=> [8,3,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
=> [8,2,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,4] => ? = 5 + 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
=> [3,3,1,1,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
=> [9,4]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
=> [8,3,2]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
=> [9,5]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]
=> [8,4,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,6] => ? = 3 + 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]
=> [8,3,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,5] => ? = 4 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
=> [9,6]
=> [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,7] => ? = 2 + 1
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> [2,2,2,2,2,2,1,1,1]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]
=> [10] => ? = 0 + 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
=> [9,7]
=> [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,8] => ? = 1 + 1
Description
The maximal number of repetitions of an integer composition.
Matching statistic: St001640
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St001640: Permutations ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 70%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St001640: Permutations ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 70%
Values
[1,0,1,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,3,2] => 0
[1,0,1,1,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2,1] => 0
[1,1,0,0,1,0]
=> [2]
=> [1,0,1,0]
=> [1,2] => 1
[1,1,0,1,0,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => 0
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => 0
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3,4,2] => 0
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [2,3,1] => 0
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,4,3,2] => 0
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,1,0,0,0]
=> [3,2,1] => 0
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,2,4,3] => 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,1,0,0]
=> [1,3,2] => 0
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,1,0,0]
=> [2,1] => 0
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,0,1,0,1,0]
=> [1,2,3] => 2
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,0,1,0]
=> [1,2] => 1
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0]
=> [1] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,4,6,5,3,7,2] => ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,5,4,2,6,1] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,2,6,5,4,7,3] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,5,4,3,6,2] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,4,5,3,6,7,2] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [3,4,2,5,6,1] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,2,5,4,6,7,3] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,4,3,5,6,2] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,4] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [2,3,4,1] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,4,6,5,3,2] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,5,4,2,1] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,2,6,5,4,3] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,4,5,3,6,2] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,4,2,5,1] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,2,5,4,6,3] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3,4,2] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [2,3,1] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,3,2] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [3,4,2,1] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,4,3,2] => 0
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,1,0,0,0]
=> [3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,4,7,6,8,5,3,9,2] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> [3,6,5,7,4,2,8,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,2,7,6,8,5,4,9,3] => ? = 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [1,6,5,7,4,3,8,2] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [5,4,6,3,2,7,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,4,5,7,8,6,3,9,2] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [3,4,6,7,5,2,8,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,2,5,7,8,6,4,9,3] => ? = 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,4,6,7,5,3,8,2] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [3,5,6,4,2,7,1] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,2,3,7,8,6,5,9,4] => ? = 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,2,6,7,5,4,8,3] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,5,6,4,3,7,2] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,4,7,6,5,3,8,9,2] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [3,6,5,4,2,7,8,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,2,7,6,5,4,8,9,3] => ? = 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,6,5,4,3,7,8,2] => ? = 0
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [5,4,3,2,6,7,1] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,4,5,7,6,3,8,9,2] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [3,4,6,5,2,7,8,1] => ? = 0
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,7,6,4,8,9,3] => ? = 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,4,6,5,3,7,8,2] => ? = 0
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [3,5,4,2,6,7,1] => ? = 0
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,3,7,6,5,8,9,4] => ? = 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,6,5,4,7,8,3] => ? = 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1,1]
=> [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,5,4,3,6,7,2] => ? = 0
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,4,5,6,3,7,8,9,2] => ? = 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [3,4,5,2,6,7,8,1] => ? = 0
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,2,5,6,4,7,8,9,3] => ? = 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,4,5,3,6,7,8,2] => ? = 0
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [3,4,2,5,6,7,1] => ? = 0
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,1,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,2,3,6,5,7,8,9,4] => ? = 2
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,2,5,4,6,7,8,3] => ? = 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [5,1,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,3,4,6,7,8,9,5] => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [4,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,8,4] => ? = 2
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [1,4,7,6,8,5,3,2] => ? = 0
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [3,6,5,7,4,2,1] => ? = 0
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,2,7,6,8,5,4,3] => ? = 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,6,5,7,4,3,2] => ? = 0
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,4,5,7,8,6,3,2] => ? = 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,4,6,7,5,2,1] => ? = 0
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,2,5,7,8,6,4,3] => ? = 1
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,4,6,7,5,3,2] => ? = 0
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,2,3,7,8,6,5,4] => ? = 2
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1]
=> [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,4,7,6,5,3,8,2] => ? = 0
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [3,6,5,4,2,7,1] => ? = 0
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,7,6,5,4,8,3] => ? = 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,6,5,4,3,7,2] => ? = 0
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> [1,4,5,7,6,3,8,2] => ? = 0
Description
The number of ascent tops in the permutation such that all smaller elements appear before.
Matching statistic: St000078
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000078: Permutations ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 60%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000078: Permutations ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 60%
Values
[1,0,1,0]
=> [2,1] => [2,1] => 1 = 0 + 1
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => 1 = 0 + 1
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => 1 = 0 + 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => 2 = 1 + 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => 2 = 1 + 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => 3 = 2 + 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => 3 = 2 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => 2 = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => 2 = 1 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => 3 = 2 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => 2 = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 0 + 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => ? = 0 + 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => ? = 0 + 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => ? = 0 + 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [6,7,5,3,2,4,1] => [7,6,5,3,2,4,1] => ? = 0 + 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => ? = 0 + 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => ? = 0 + 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => ? = 0 + 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => ? = 0 + 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => ? = 0 + 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => ? = 0 + 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => ? = 0 + 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,7,1] => [4,3,5,2,6,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,5,1] => [7,6,2,3,4,5,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => ? = 1 + 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [5,4,2,3,6,7,1] => [4,5,2,3,6,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,7,1] => [4,3,2,5,6,7,1] => ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,3,1,2] => [7,6,5,4,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => ? = 1 + 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,4,1,2] => [6,5,7,3,4,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,5,1,2] => [7,6,3,4,5,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,2,1,3] => [7,6,5,4,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,1,3] => [5,4,6,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [7,6,5,3,2,1,4] => [6,7,5,3,2,1,4] => ? = 0 + 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,2,1,4] => [6,5,7,3,2,1,4] => ? = 0 + 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => ? = 1 + 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [6,5,4,3,2,1,7] => [5,6,4,3,2,1,7] => ? = 0 + 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,2,1,7] => [6,5,4,3,2,1,7] => ? = 0 + 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [6,4,5,3,2,1,7] => [4,6,5,3,2,1,7] => ? = 1 + 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,2,1,7] => [4,5,6,3,2,1,7] => ? = 0 + 1
Description
The number of alternating sign matrices whose left key is the permutation.
The left key of an alternating sign matrix was defined by Lascoux
in [2] and is obtained by successively removing all the `-1`'s until what remains is a permutation matrix. This notion corresponds to the notion of left key for semistandard tableaux.
Matching statistic: St000356
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000356: Permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 70%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000356: Permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 70%
Values
[1,0,1,0]
=> [2,1] => [2,1] => 0
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => 0
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => 0
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => 0
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => 0
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => 0
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => 0
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => 0
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => 0
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => 0
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => 0
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => 2
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => ? = 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => ? = 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [3,4,5,6,7,2,1] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [6,7,5,3,2,4,1] => [7,6,5,3,2,4,1] => ? = 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => ? = 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => ? = 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => ? = 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => ? = 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => ? = 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => ? = 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => ? = 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,5,1] => [7,6,2,3,4,5,1] => ? = 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => ? = 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => ? = 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => ? = 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => ? = 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [2,6,3,4,5,7,1] => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [2,5,3,4,6,7,1] => ? = 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => ? = 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => ? = 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => ? = 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => ? = 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => ? = 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,5,1,2] => [7,6,3,4,5,1,2] => ? = 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => ? = 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,5,4,6,7,1,2] => ? = 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => ? = 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,2,1,3] => [7,6,5,4,2,1,3] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,1,3] => [5,4,6,7,2,1,3] => ? = 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [7,6,5,3,2,1,4] => [6,7,5,3,2,1,4] => ? = 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,2,1,4] => [6,5,7,3,2,1,4] => ? = 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => ? = 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,2,1,7] => [5,6,3,4,2,1,7] => ? = 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => ? = 1
Description
The number of occurrences of the pattern 13-2.
See [[Permutations/#Pattern-avoiding_permutations]] for the definition of the pattern $13\!\!-\!\!2$.
Matching statistic: St000220
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000220: Permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 70%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000220: Permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 70%
Values
[1,0,1,0]
=> [2,1] => [2,1] => 0
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => 0
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => 0
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => 0
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => 0
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => 0
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => 0
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => 0
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => 0
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => 0
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => 0
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => 2
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => ? = 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => ? = 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [3,4,5,6,7,2,1] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [6,7,5,3,2,4,1] => [7,6,5,3,2,4,1] => ? = 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => ? = 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => ? = 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => ? = 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => ? = 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => ? = 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => ? = 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => ? = 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,5,1] => [7,6,2,3,4,5,1] => ? = 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => ? = 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => ? = 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => ? = 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => ? = 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [2,6,3,4,5,7,1] => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [2,5,3,4,6,7,1] => ? = 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => ? = 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => ? = 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => ? = 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => ? = 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => ? = 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => ? = 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,5,1,2] => [7,6,3,4,5,1,2] => ? = 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => ? = 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => ? = 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,5,4,6,7,1,2] => ? = 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => ? = 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,2,1,3] => [7,6,5,4,2,1,3] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => ? = 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,1,3] => [5,4,6,7,2,1,3] => ? = 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [7,6,5,3,2,1,4] => [6,7,5,3,2,1,4] => ? = 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,2,1,4] => [6,5,7,3,2,1,4] => ? = 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => ? = 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,2,1,7] => [5,6,3,4,2,1,7] => ? = 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => ? = 1
Description
The number of occurrences of the pattern 132 in a permutation.
Matching statistic: St000255
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000255: Permutations ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 60%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
St000255: Permutations ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 60%
Values
[1,0,1,0]
=> [2,1] => [2,1] => 1 = 0 + 1
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => 1 = 0 + 1
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => 1 = 0 + 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => 2 = 1 + 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => 1 = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => 2 = 1 + 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => 3 = 2 + 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => 1 = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => 1 = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => 3 = 2 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => 2 = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => 2 = 1 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => 3 = 2 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => 2 = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,3,2,1] => [7,6,5,4,3,2,1] => ? = 0 + 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => ? = 0 + 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => ? = 0 + 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => ? = 0 + 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => ? = 1 + 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [3,4,5,6,7,2,1] => ? = 0 + 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => ? = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [6,7,5,3,2,4,1] => [7,6,5,3,2,4,1] => ? = 0 + 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => ? = 0 + 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => ? = 0 + 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => ? = 1 + 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => ? = 0 + 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => ? = 0 + 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => ? = 0 + 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => ? = 0 + 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,5,1] => [7,6,2,3,4,5,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => ? = 1 + 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => ? = 0 + 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => ? = 1 + 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [2,6,3,4,5,7,1] => ? = 3 + 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [2,5,3,4,6,7,1] => ? = 2 + 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => ? = 1 + 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,3,1,2] => [7,6,5,4,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => ? = 1 + 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,4,1,2] => [6,5,7,3,4,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> [6,7,3,4,5,1,2] => [7,6,3,4,5,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => ? = 0 + 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,5,4,6,7,1,2] => ? = 1 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> [6,7,5,4,2,1,3] => [7,6,5,4,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,1,3] => [5,4,6,7,2,1,3] => ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [7,6,5,3,2,1,4] => [6,7,5,3,2,1,4] => ? = 0 + 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,2,1,4] => [6,5,7,3,2,1,4] => ? = 0 + 1
Description
The number of reduced Kogan faces with the permutation as type.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
Matching statistic: St000358
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000358: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 50%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000358: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0]
=> [2,1] => [2,1] => [1,2] => 0
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => [2,1,3] => 0
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => [1,2,3] => 0
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => [3,1,2] => 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => [2,3,1] => 0
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => [2,1,3,4] => 0
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => [3,1,2,4] => 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => [3,2,1,4] => 0
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => [2,3,1,4] => 0
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => [2,1,4,3] => 0
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => [1,2,4,3] => 0
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => [3,1,4,2] => 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => [3,2,4,1] => 0
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => [2,3,4,1] => 0
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => [4,1,3,2] => 2
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => [4,2,3,1] => 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => [3,4,2,1] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => [2,1,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => [3,1,2,4,5] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => [3,2,1,4,5] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => [2,3,1,4,5] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => [2,1,4,3,5] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => [1,2,4,3,5] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => [3,1,4,2,5] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => [3,2,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => [2,3,4,1,5] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => [4,1,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => [4,2,3,1,5] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => [4,3,2,1,5] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => [3,4,2,1,5] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => [2,1,3,5,4] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => [1,2,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => [3,1,2,5,4] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => [3,2,1,5,4] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => [2,3,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => [2,1,4,5,3] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => [1,2,4,5,3] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => [3,1,4,5,2] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => [3,2,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => [2,3,4,5,1] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => [4,1,3,5,2] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => [4,2,3,5,1] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => [4,3,2,5,1] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => [3,4,2,5,1] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => [2,1,5,4,3] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => [1,2,5,4,3] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => [3,1,5,4,2] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => [5,3,4,2,1,6,7] => ? = 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => ? = 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => ? = 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => ? = 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => [5,3,4,2,6,1,7] => ? = 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,7,1] => [3,4,5,6,2,7,1] => [5,4,3,2,6,1,7] => ? = 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => [4,5,3,2,6,1,7] => ? = 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => ? = 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => [3,4,5,6,2,1,7] => ? = 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,3,5,2,6,7,1] => [3,4,5,2,6,7,1] => [5,4,3,6,2,1,7] => ? = 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,7,1] => [4,3,5,2,6,7,1] => [4,5,3,6,2,1,7] => ? = 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => ? = 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => [4,2,6,5,3,1,7] => ? = 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [5,4,2,3,6,7,1] => [4,5,2,3,6,7,1] => [4,3,6,5,2,1,7] => ? = 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => ? = 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [5,3,6,4,2,1,7] => ? = 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [4,3,2,5,6,7,1] => [3,4,2,5,6,7,1] => [5,4,6,3,2,1,7] => ? = 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,7,1] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => ? = 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [2,6,3,4,5,7,1] => [6,2,5,4,3,1,7] => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [2,5,3,4,6,7,1] => [6,3,5,4,2,1,7] => ? = 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [6,4,5,3,2,1,7] => ? = 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [3,2,4,5,6,7,1] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => ? = 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [3,2,4,5,6,7,1] => [5,6,4,3,2,1,7] => ? = 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => [2,3,1,4,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => [2,3,4,1,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => [4,2,3,1,5,7,6] => ? = 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => [3,4,2,1,5,7,6] => ? = 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,4,1,2] => [6,5,7,3,4,1,2] => [2,3,1,5,4,7,6] => ? = 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => ? = 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => [4,3,2,5,1,7,6] => ? = 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => [3,4,2,5,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => [2,3,5,4,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => [4,3,5,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => [3,4,5,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,5,4,6,7,1,2] => [5,3,4,2,1,7,6] => ? = 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,1,2] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => [4,5,3,2,1,7,6] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => [2,3,1,4,6,7,5] => ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => [2,3,4,1,6,7,5] => ? = 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => [4,3,2,1,6,7,5] => ? = 0
Description
The number of occurrences of the pattern 31-2.
See [[Permutations/#Pattern-avoiding_permutations]] for the definition of the pattern $31\!\!-\!\!2$.
Matching statistic: St000801
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000801: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 50%
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000801: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0]
=> [2,1] => [2,1] => [1,2] => 0
[1,0,1,0,1,0]
=> [3,2,1] => [2,3,1] => [2,1,3] => 0
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => [1,2,3] => 0
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => [3,1,2] => 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => [2,3,1] => 0
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [3,4,2,1] => [2,1,3,4] => 0
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [2,4,3,1] => [3,1,2,4] => 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [2,3,4,1] => [3,2,1,4] => 0
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [3,2,4,1] => [2,3,1,4] => 0
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [3,4,1,2] => [2,1,4,3] => 0
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [4,3,1,2] => [1,2,4,3] => 0
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [2,4,1,3] => [3,1,4,2] => 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [2,3,1,4] => [3,2,4,1] => 0
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,2,1,4] => [2,3,4,1] => 0
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,4,2,3] => [4,1,3,2] => 2
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => [4,2,3,1] => 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => [3,4,2,1] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [4,5,3,2,1] => [2,1,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [3,5,4,2,1] => [3,1,2,4,5] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [3,4,5,2,1] => [3,2,1,4,5] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [4,3,5,2,1] => [2,3,1,4,5] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [4,5,2,3,1] => [2,1,4,3,5] => 0
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,4,2,3,1] => [1,2,4,3,5] => 0
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [3,5,2,4,1] => [3,1,4,2,5] => 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [3,4,2,5,1] => [3,2,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [4,3,2,5,1] => [2,3,4,1,5] => 0
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [2,5,3,4,1] => [4,1,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [2,4,3,5,1] => [4,2,3,1,5] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [2,3,4,5,1] => [4,3,2,1,5] => 0
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [3,2,4,5,1] => [3,4,2,1,5] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [4,5,3,1,2] => [2,1,3,5,4] => 0
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [5,4,3,1,2] => [1,2,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [3,5,4,1,2] => [3,1,2,5,4] => 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [3,4,5,1,2] => [3,2,1,5,4] => 0
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [4,3,5,1,2] => [2,3,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,5,2,1,3] => [2,1,4,5,3] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [5,4,2,1,3] => [1,2,4,5,3] => 0
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [3,5,2,1,4] => [3,1,4,5,2] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [3,4,2,1,5] => [3,2,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,2,1,5] => [2,3,4,5,1] => 0
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [2,5,3,1,4] => [4,1,3,5,2] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [2,4,3,1,5] => [4,2,3,5,1] => 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [2,3,4,1,5] => [4,3,2,5,1] => 0
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [3,2,4,1,5] => [3,4,2,5,1] => 0
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [4,5,1,2,3] => [2,1,5,4,3] => 0
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [5,4,1,2,3] => [1,2,5,4,3] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,5,1,2,4] => [3,1,5,4,2] => 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [3,4,1,2,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => [5,3,4,2,1,6,7] => ? = 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,3,1] => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,3,1] => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => ? = 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => ? = 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => ? = 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => [5,3,4,2,6,1,7] => ? = 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,7,1] => [3,4,5,6,2,7,1] => [5,4,3,2,6,1,7] => ? = 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [4,3,5,6,2,7,1] => [4,5,3,2,6,1,7] => ? = 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,7,1] => [6,5,4,2,3,7,1] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => ? = 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,7,1] => [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => ? = 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [5,4,3,2,6,7,1] => [3,4,5,6,2,1,7] => ? = 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,3,5,2,6,7,1] => [3,4,5,2,6,7,1] => [5,4,3,6,2,1,7] => ? = 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,7,1] => [4,3,5,2,6,7,1] => [4,5,3,6,2,1,7] => ? = 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => ? = 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,7,1] => [4,6,2,3,5,7,1] => [4,2,6,5,3,1,7] => ? = 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [5,4,2,3,6,7,1] => [4,5,2,3,6,7,1] => [4,3,6,5,2,1,7] => ? = 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => ? = 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [5,3,6,4,2,1,7] => ? = 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [4,3,2,5,6,7,1] => [3,4,2,5,6,7,1] => [5,4,6,3,2,1,7] => ? = 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,7,1] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => ? = 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [2,6,3,4,5,7,1] => [6,2,5,4,3,1,7] => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [2,5,3,4,6,7,1] => [6,3,5,4,2,1,7] => ? = 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [6,4,5,3,2,1,7] => ? = 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [3,2,4,5,6,7,1] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => ? = 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [3,2,4,5,6,7,1] => [5,6,4,3,2,1,7] => ? = 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,3,1,2] => [6,5,7,4,3,1,2] => [2,3,1,4,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,3,1,2] => [6,5,4,7,3,1,2] => [2,3,4,1,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [6,4,5,7,3,1,2] => [4,6,5,7,3,1,2] => [4,2,3,1,5,7,6] => ? = 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,3,1,2] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => ? = 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [5,4,6,7,3,1,2] => [3,4,2,1,5,7,6] => ? = 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [5,6,7,3,4,1,2] => [6,5,7,3,4,1,2] => [2,3,1,5,4,7,6] => ? = 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,7,1,2] => [6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => ? = 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,7,1,2] => [4,5,6,3,7,1,2] => [4,3,2,5,1,7,6] => ? = 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [5,4,6,3,7,1,2] => [3,4,2,5,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,7,1,2] => [6,5,3,4,7,1,2] => [2,3,5,4,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,7,1,2] => [4,5,3,6,7,1,2] => [4,3,5,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [5,4,3,6,7,1,2] => [3,4,5,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,5,4,6,7,1,2] => [5,3,4,2,1,7,6] => ? = 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,1,2] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => ? = 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [4,3,5,6,7,1,2] => [4,5,3,2,1,7,6] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=> [5,6,7,4,2,1,3] => [6,5,7,4,2,1,3] => [2,3,1,4,6,7,5] => ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [5,6,4,7,2,1,3] => [6,5,4,7,2,1,3] => [2,3,4,1,6,7,5] => ? = 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [5,4,6,7,2,1,3] => [4,5,6,7,2,1,3] => [4,3,2,1,6,7,5] => ? = 0
Description
The number of occurrences of the vincular pattern |312 in a permutation.
This is the number of occurrences of the pattern $(3,1,2)$, such that the letter matched by $3$ is the first entry of the permutation.
The following 12 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000217The number of occurrences of the pattern 312 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000260The radius of a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000259The diameter of a connected graph. St001330The hat guessing number of a graph. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001964The interval resolution global dimension of a poset. St001876The number of 2-regular simple modules in the incidence algebra of the lattice.
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!