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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001092
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001092: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001092: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> []
=> []
=> 0
[2]
=> []
=> []
=> 0
[1,1]
=> [1]
=> [1]
=> 0
[3]
=> []
=> []
=> 0
[2,1]
=> [1]
=> [1]
=> 0
[1,1,1]
=> [1,1]
=> [2]
=> 1
[4]
=> []
=> []
=> 0
[3,1]
=> [1]
=> [1]
=> 0
[2,2]
=> [2]
=> [1,1]
=> 0
[2,1,1]
=> [1,1]
=> [2]
=> 1
[1,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[5]
=> []
=> []
=> 0
[4,1]
=> [1]
=> [1]
=> 0
[3,2]
=> [2]
=> [1,1]
=> 0
[3,1,1]
=> [1,1]
=> [2]
=> 1
[2,2,1]
=> [2,1]
=> [2,1]
=> 1
[2,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[1,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[6]
=> []
=> []
=> 0
[5,1]
=> [1]
=> [1]
=> 0
[4,2]
=> [2]
=> [1,1]
=> 0
[4,1,1]
=> [1,1]
=> [2]
=> 1
[3,3]
=> [3]
=> [1,1,1]
=> 0
[3,2,1]
=> [2,1]
=> [2,1]
=> 1
[3,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[2,2,2]
=> [2,2]
=> [2,2]
=> 1
[2,2,1,1]
=> [2,1,1]
=> [3,1]
=> 0
[2,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> 0
[7]
=> []
=> []
=> 0
[6,1]
=> [1]
=> [1]
=> 0
[5,2]
=> [2]
=> [1,1]
=> 0
[5,1,1]
=> [1,1]
=> [2]
=> 1
[4,3]
=> [3]
=> [1,1,1]
=> 0
[4,2,1]
=> [2,1]
=> [2,1]
=> 1
[4,1,1,1]
=> [1,1,1]
=> [3]
=> 0
[3,3,1]
=> [3,1]
=> [2,1,1]
=> 1
[3,2,2]
=> [2,2]
=> [2,2]
=> 1
[3,2,1,1]
=> [2,1,1]
=> [3,1]
=> 0
[3,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> 1
[2,2,2,1]
=> [2,2,1]
=> [3,2]
=> 1
[2,2,1,1,1]
=> [2,1,1,1]
=> [4,1]
=> 1
[2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> 0
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [6]
=> 1
[8]
=> []
=> []
=> 0
[7,1]
=> [1]
=> [1]
=> 0
[6,2]
=> [2]
=> [1,1]
=> 0
[6,1,1]
=> [1,1]
=> [2]
=> 1
[5,3]
=> [3]
=> [1,1,1]
=> 0
[5,2,1]
=> [2,1]
=> [2,1]
=> 1
Description
The number of distinct even parts of a partition.
See Section 3.3.1 of [1].
Matching statistic: St000257
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000257: Integer partitions ⟶ ℤResult quality: 67% ●values known / values provided: 86%●distinct values known / distinct values provided: 67%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000257: Integer partitions ⟶ ℤResult quality: 67% ●values known / values provided: 86%●distinct values known / distinct values provided: 67%
Values
[1]
=> []
=> []
=> ?
=> ? = 0
[2]
=> []
=> []
=> ?
=> ? = 0
[1,1]
=> [1]
=> [1]
=> [1]
=> 0
[3]
=> []
=> []
=> ?
=> ? = 0
[2,1]
=> [1]
=> [1]
=> [1]
=> 0
[1,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[4]
=> []
=> []
=> ?
=> ? = 0
[3,1]
=> [1]
=> [1]
=> [1]
=> 0
[2,2]
=> [2]
=> [1,1]
=> [2]
=> 0
[2,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[1,1,1,1]
=> [1,1,1]
=> [3]
=> [3]
=> 0
[5]
=> []
=> []
=> ?
=> ? = 0
[4,1]
=> [1]
=> [1]
=> [1]
=> 0
[3,2]
=> [2]
=> [1,1]
=> [2]
=> 0
[3,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[2,2,1]
=> [2,1]
=> [2,1]
=> [1,1,1]
=> 1
[2,1,1,1]
=> [1,1,1]
=> [3]
=> [3]
=> 0
[1,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> [2,2]
=> 1
[6]
=> []
=> []
=> ?
=> ? = 0
[5,1]
=> [1]
=> [1]
=> [1]
=> 0
[4,2]
=> [2]
=> [1,1]
=> [2]
=> 0
[4,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[3,3]
=> [3]
=> [1,1,1]
=> [2,1]
=> 0
[3,2,1]
=> [2,1]
=> [2,1]
=> [1,1,1]
=> 1
[3,1,1,1]
=> [1,1,1]
=> [3]
=> [3]
=> 0
[2,2,2]
=> [2,2]
=> [2,2]
=> [1,1,1,1]
=> 1
[2,2,1,1]
=> [2,1,1]
=> [3,1]
=> [3,1]
=> 0
[2,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> [2,2]
=> 1
[1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> [5]
=> 0
[7]
=> []
=> []
=> ?
=> ? = 0
[6,1]
=> [1]
=> [1]
=> [1]
=> 0
[5,2]
=> [2]
=> [1,1]
=> [2]
=> 0
[5,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[4,3]
=> [3]
=> [1,1,1]
=> [2,1]
=> 0
[4,2,1]
=> [2,1]
=> [2,1]
=> [1,1,1]
=> 1
[4,1,1,1]
=> [1,1,1]
=> [3]
=> [3]
=> 0
[3,3,1]
=> [3,1]
=> [2,1,1]
=> [2,1,1]
=> 1
[3,2,2]
=> [2,2]
=> [2,2]
=> [1,1,1,1]
=> 1
[3,2,1,1]
=> [2,1,1]
=> [3,1]
=> [3,1]
=> 0
[3,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> [2,2]
=> 1
[2,2,2,1]
=> [2,2,1]
=> [3,2]
=> [3,1,1]
=> 1
[2,2,1,1,1]
=> [2,1,1,1]
=> [4,1]
=> [2,2,1]
=> 1
[2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [5]
=> [5]
=> 0
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [6]
=> [3,3]
=> 1
[8]
=> []
=> []
=> ?
=> ? = 0
[7,1]
=> [1]
=> [1]
=> [1]
=> 0
[6,2]
=> [2]
=> [1,1]
=> [2]
=> 0
[6,1,1]
=> [1,1]
=> [2]
=> [1,1]
=> 1
[5,3]
=> [3]
=> [1,1,1]
=> [2,1]
=> 0
[5,2,1]
=> [2,1]
=> [2,1]
=> [1,1,1]
=> 1
[5,1,1,1]
=> [1,1,1]
=> [3]
=> [3]
=> 0
[4,4]
=> [4]
=> [1,1,1,1]
=> [4]
=> 0
[4,3,1]
=> [3,1]
=> [2,1,1]
=> [2,1,1]
=> 1
[4,2,2]
=> [2,2]
=> [2,2]
=> [1,1,1,1]
=> 1
[4,2,1,1]
=> [2,1,1]
=> [3,1]
=> [3,1]
=> 0
[4,1,1,1,1]
=> [1,1,1,1]
=> [4]
=> [2,2]
=> 1
[3,3,2]
=> [3,2]
=> [2,2,1]
=> [1,1,1,1,1]
=> 1
[3,3,1,1]
=> [3,1,1]
=> [3,1,1]
=> [3,2]
=> 0
[9]
=> []
=> []
=> ?
=> ? = 0
[10]
=> []
=> []
=> ?
=> ? = 0
[11]
=> []
=> []
=> ?
=> ? = 0
[12]
=> []
=> []
=> ?
=> ? = 0
[13]
=> []
=> []
=> ?
=> ? = 0
[14]
=> []
=> []
=> ?
=> ? = 0
[3,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [7,3,1]
=> [7,3,1]
=> ? = 0
[3,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [9,1,1]
=> [9,2]
=> ? = 0
[15]
=> []
=> []
=> ?
=> ? = 0
[4,4,2,1,1,1,1,1]
=> [4,2,1,1,1,1,1]
=> [7,2,1,1]
=> [7,2,1,1]
=> ? = 1
[4,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [7,3,1]
=> [7,3,1]
=> ? = 0
[4,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [9,1,1]
=> [9,2]
=> ? = 0
[3,3,3,2,1,1,1,1]
=> [3,3,2,1,1,1,1]
=> [7,3,2]
=> [7,3,1,1]
=> ? = 1
[3,3,3,1,1,1,1,1,1]
=> [3,3,1,1,1,1,1,1]
=> [8,2,2]
=> [4,4,1,1,1,1]
=> ? = 2
[3,3,2,2,2,1,1,1]
=> [3,2,2,2,1,1,1]
=> [7,4,1]
=> [7,2,2,1]
=> ? = 1
[3,3,2,1,1,1,1,1,1,1]
=> [3,2,1,1,1,1,1,1,1]
=> [9,2,1]
=> [9,1,1,1]
=> ? = 1
[16]
=> []
=> []
=> ?
=> ? = 0
[5,5,2,1,1,1,1]
=> [5,2,1,1,1,1]
=> [6,2,1,1,1]
=> [3,3,2,1,1,1]
=> ? = 2
[5,4,2,1,1,1,1,1]
=> [4,2,1,1,1,1,1]
=> [7,2,1,1]
=> [7,2,1,1]
=> ? = 1
[5,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [7,3,1]
=> [7,3,1]
=> ? = 0
[5,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [9,1,1]
=> [9,2]
=> ? = 0
[4,4,3,2,1,1,1]
=> [4,3,2,1,1,1]
=> [6,3,2,1]
=> [3,3,3,1,1,1]
=> ? = 2
[4,4,3,1,1,1,1,1]
=> [4,3,1,1,1,1,1]
=> [7,2,2,1]
=> [7,1,1,1,1,1]
=> ? = 1
[4,4,2,2,1,1,1,1]
=> [4,2,2,1,1,1,1]
=> [7,3,1,1]
=> [7,3,2]
=> ? = 0
[4,4,1,1,1,1,1,1,1,1]
=> [4,1,1,1,1,1,1,1,1]
=> [9,1,1,1]
=> [9,2,1]
=> ? = 0
[4,3,3,2,1,1,1,1]
=> [3,3,2,1,1,1,1]
=> [7,3,2]
=> [7,3,1,1]
=> ? = 1
[4,3,3,1,1,1,1,1,1]
=> [3,3,1,1,1,1,1,1]
=> [8,2,2]
=> [4,4,1,1,1,1]
=> ? = 2
[4,3,2,2,2,1,1,1]
=> [3,2,2,2,1,1,1]
=> [7,4,1]
=> [7,2,2,1]
=> ? = 1
[4,3,2,1,1,1,1,1,1,1]
=> [3,2,1,1,1,1,1,1,1]
=> [9,2,1]
=> [9,1,1,1]
=> ? = 1
[3,3,3,3,3,1]
=> [3,3,3,3,1]
=> [5,4,4]
=> [5,2,2,2,2]
=> ? = 1
[3,3,3,2,2,1,1,1]
=> [3,3,2,2,1,1,1]
=> [7,4,2]
=> [7,2,2,1,1]
=> ? = 2
[3,3,3,1,1,1,1,1,1,1]
=> [3,3,1,1,1,1,1,1,1]
=> [9,2,2]
=> [9,1,1,1,1]
=> ? = 1
[17]
=> []
=> []
=> ?
=> ? = 0
[6,6,3,2]
=> [6,3,2]
=> [3,3,2,1,1,1]
=> [6,2,1,1,1]
=> ? = 1
[6,5,2,1,1,1,1]
=> [5,2,1,1,1,1]
=> [6,2,1,1,1]
=> [3,3,2,1,1,1]
=> ? = 2
[6,4,2,1,1,1,1,1]
=> [4,2,1,1,1,1,1]
=> [7,2,1,1]
=> [7,2,1,1]
=> ? = 1
[6,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [7,3,1]
=> [7,3,1]
=> ? = 0
[6,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [9,1,1]
=> [9,2]
=> ? = 0
[5,5,3,1,1,1,1]
=> [5,3,1,1,1,1]
=> [6,2,2,1,1]
=> [3,3,2,1,1,1,1]
=> ? = 2
[5,5,2,1,1,1,1,1]
=> [5,2,1,1,1,1,1]
=> [7,2,1,1,1]
=> [7,2,1,1,1]
=> ? = 1
[5,4,3,2,1,1,1]
=> [4,3,2,1,1,1]
=> [6,3,2,1]
=> [3,3,3,1,1,1]
=> ? = 2
[5,4,3,1,1,1,1,1]
=> [4,3,1,1,1,1,1]
=> [7,2,2,1]
=> [7,1,1,1,1,1]
=> ? = 1
Description
The number of distinct parts of a partition that occur at least twice.
See Section 3.3.1 of [2].
Matching statistic: St001115
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001115: Permutations ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 83%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001115: Permutations ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 83%
Values
[1]
=> []
=> []
=> [] => 0
[2]
=> []
=> []
=> [] => 0
[1,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[3]
=> []
=> []
=> [] => 0
[2,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[1,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[4]
=> []
=> []
=> [] => 0
[3,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[2,2]
=> [2]
=> [1,1,0,0,1,0]
=> [3,1,2] => 0
[2,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[1,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [2,3,4,1] => 0
[5]
=> []
=> []
=> [] => 0
[4,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[3,2]
=> [2]
=> [1,1,0,0,1,0]
=> [3,1,2] => 0
[3,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[2,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> [3,2,1] => 1
[2,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [2,3,4,1] => 0
[1,1,1,1,1]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 1
[6]
=> []
=> []
=> [] => 0
[5,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[4,2]
=> [2]
=> [1,1,0,0,1,0]
=> [3,1,2] => 0
[4,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[3,3]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [4,1,2,3] => 0
[3,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> [3,2,1] => 1
[3,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [2,3,4,1] => 0
[2,2,2]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [3,4,1,2] => 1
[2,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [3,2,4,1] => 0
[2,1,1,1,1]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 1
[1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => 0
[7]
=> []
=> []
=> [] => 0
[6,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[5,2]
=> [2]
=> [1,1,0,0,1,0]
=> [3,1,2] => 0
[5,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[4,3]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [4,1,2,3] => 0
[4,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> [3,2,1] => 1
[4,1,1,1]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [2,3,4,1] => 0
[3,3,1]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [4,2,1,3] => 1
[3,2,2]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [3,4,1,2] => 1
[3,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [3,2,4,1] => 0
[3,1,1,1,1]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 1
[2,2,2,1]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 1
[2,2,1,1,1]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => 1
[2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => 0
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => 1
[8]
=> []
=> []
=> [] => 0
[7,1]
=> [1]
=> [1,0,1,0]
=> [2,1] => 0
[6,2]
=> [2]
=> [1,1,0,0,1,0]
=> [3,1,2] => 0
[6,1,1]
=> [1,1]
=> [1,0,1,1,0,0]
=> [2,3,1] => 1
[5,3]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [4,1,2,3] => 0
[5,2,1]
=> [2,1]
=> [1,0,1,0,1,0]
=> [3,2,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 0
[2,2,2,2,2,2,1]
=> [2,2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => ? = 1
[2,2,2,2,2,1,1,1]
=> [2,2,2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,2,7,8,1] => ? = 1
[2,2,2,2,1,1,1,1,1]
=> [2,2,2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
=> [3,4,5,2,6,7,8,9,1] => ? = 1
[2,2,2,1,1,1,1,1,1,1]
=> [2,2,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [3,4,2,5,6,7,8,9,10,1] => ? = 1
[2,2,1,1,1,1,1,1,1,1,1]
=> [2,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
=> [3,2,4,5,6,7,8,9,10,11,1] => ? = 1
[2,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 0
[1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 1
[3,3,3,2,1,1,1]
=> [3,3,2,1,1,1]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => ? = 2
[3,3,3,1,1,1,1,1]
=> [3,3,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [4,5,2,3,6,7,8,1] => ? = 1
[3,3,2,2,2,2]
=> [3,2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,1,2] => ? = 0
[3,3,2,2,2,1,1]
=> [3,2,2,2,1,1]
=> [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,7,1] => ? = 2
[3,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [4,3,5,2,6,7,8,1] => ? = 0
[3,3,2,1,1,1,1,1,1]
=> [3,2,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [4,3,2,5,6,7,8,9,1] => ? = 2
[3,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
=> [4,2,3,5,6,7,8,9,10,1] => ? = 0
[3,2,2,2,2,2,1]
=> [2,2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => ? = 1
[3,2,2,2,2,1,1,1]
=> [2,2,2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,2,7,8,1] => ? = 1
[3,2,2,2,1,1,1,1,1]
=> [2,2,2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
=> [3,4,5,2,6,7,8,9,1] => ? = 1
[3,2,2,1,1,1,1,1,1,1]
=> [2,2,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [3,4,2,5,6,7,8,9,10,1] => ? = 1
[3,2,1,1,1,1,1,1,1,1,1]
=> [2,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
=> [3,2,4,5,6,7,8,9,10,11,1] => ? = 1
[3,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 0
[2,2,2,2,2,2,1,1]
=> [2,2,2,2,2,1,1]
=> [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,7,2,8,1] => ? = 0
[2,2,2,2,2,1,1,1,1]
=> [2,2,2,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
=> [3,4,5,6,2,7,8,9,1] => ? = 2
[2,2,2,2,1,1,1,1,1,1]
=> [2,2,2,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
=> [3,4,5,2,6,7,8,9,10,1] => ? = 0
[2,2,2,1,1,1,1,1,1,1,1]
=> [2,2,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
=> [3,4,2,5,6,7,8,9,10,11,1] => ? = 2
[2,2,1,1,1,1,1,1,1,1,1,1]
=> [2,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> [3,2,4,5,6,7,8,9,10,11,12,1] => ? = 0
[2,1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 0
[4,4,3,1,1,1,1]
=> [4,3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [5,4,2,3,6,7,1] => ? = 2
[4,4,2,2,1,1,1]
=> [4,2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [5,3,4,2,6,7,1] => ? = 1
[4,4,2,1,1,1,1,1]
=> [4,2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> [5,3,2,4,6,7,8,1] => ? = 1
[4,4,1,1,1,1,1,1,1]
=> [4,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
=> [5,2,3,4,6,7,8,9,1] => ? = 1
[4,3,3,2,1,1,1]
=> [3,3,2,1,1,1]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => ? = 2
[4,3,3,1,1,1,1,1]
=> [3,3,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [4,5,2,3,6,7,8,1] => ? = 1
[4,3,2,2,2,2]
=> [3,2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,1,2] => ? = 0
[4,3,2,2,2,1,1]
=> [3,2,2,2,1,1]
=> [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,7,1] => ? = 2
[4,3,2,2,1,1,1,1]
=> [3,2,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [4,3,5,2,6,7,8,1] => ? = 0
[4,3,2,1,1,1,1,1,1]
=> [3,2,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [4,3,2,5,6,7,8,9,1] => ? = 2
[4,3,1,1,1,1,1,1,1,1]
=> [3,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
=> [4,2,3,5,6,7,8,9,10,1] => ? = 0
[4,2,2,2,2,2,1]
=> [2,2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => ? = 1
[4,2,2,2,2,1,1,1]
=> [2,2,2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4,5,6,2,7,8,1] => ? = 1
[4,2,2,2,1,1,1,1,1]
=> [2,2,2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
=> [3,4,5,2,6,7,8,9,1] => ? = 1
[4,2,2,1,1,1,1,1,1,1]
=> [2,2,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
=> [3,4,2,5,6,7,8,9,10,1] => ? = 1
[4,2,1,1,1,1,1,1,1,1,1]
=> [2,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
=> [3,2,4,5,6,7,8,9,10,11,1] => ? = 1
[4,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? => ? = 0
[3,3,3,3,3]
=> [3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,1,2,3] => ? = 1
[3,3,3,3,1,1,1]
=> [3,3,3,1,1,1]
=> [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => ? = 1
[3,3,3,2,2,2]
=> [3,3,2,2,2]
=> [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => ? = 1
[3,3,3,2,2,1,1]
=> [3,3,2,2,1,1]
=> [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => ? = 3
[3,3,3,2,1,1,1,1]
=> [3,3,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [4,5,3,2,6,7,8,1] => ? = 1
Description
The number of even descents of a permutation.
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