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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000291
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000291: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000291: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1,1] => [2] => 10 => 1
[1,0,1,0,1,0]
=> [1,1,1] => [3] => 100 => 1
[1,0,1,1,0,0]
=> [1,2] => [1,1] => 11 => 0
[1,1,0,0,1,0]
=> [2,1] => [1,1] => 11 => 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [4] => 1000 => 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1] => 101 => 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [1,1,1] => 111 => 0
[1,0,1,1,0,1,0,0]
=> [1,3] => [1,1] => 11 => 0
[1,0,1,1,1,0,0,0]
=> [1,3] => [1,1] => 11 => 0
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [1,2] => 110 => 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2] => 10 => 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [1,1] => 11 => 0
[1,1,1,0,0,0,1,0]
=> [3,1] => [1,1] => 11 => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [5] => 10000 => 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [3,1] => 1001 => 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1] => 1011 => 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [2,1] => 101 => 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [2,1] => 101 => 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [1,1,2] => 1110 => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [1,2] => 110 => 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [1,1,1] => 111 => 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [1,1] => 11 => 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [1,1] => 11 => 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [1,1,1] => 111 => 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [1,1] => 11 => 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [1,1] => 11 => 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [1,1] => 11 => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => 1100 => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => 111 => 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1] => 101 => 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [1,1] => 11 => 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [1,1] => 11 => 0
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => 110 => 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [1,1] => 11 => 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [1,1] => 11 => 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [1,1] => 11 => 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => 110 => 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [1,1] => 11 => 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [1,1] => 11 => 0
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [1,1] => 11 => 0
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [1,1] => 11 => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [6] => 100000 => 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [4,1] => 10001 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [3,1,1] => 10011 => 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1] => 1001 => 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1] => 1001 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => 10110 => 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2] => 1010 => 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [2,1,1] => 1011 => 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [2,1] => 101 => 1
Description
The number of descents of a binary word.
Matching statistic: St000659
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000659: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000659: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1,1] => [2] => [1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> [1,1,1] => [3] => [1,1,1,0,0,0]
=> 1
[1,0,1,1,0,0]
=> [1,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0]
=> [2,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,0,1,0,0]
=> [1,3] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,0,0]
=> [1,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2] => [1,1,0,0]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,0,1,0]
=> [3,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [2,1] => [1,1,0,0,1,0]
=> 1
Description
The number of rises of length at least 2 of a Dyck path.
Matching statistic: St001280
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [1,1] => [2] => [2]
=> 1
[1,0,1,0,1,0]
=> [1,1,1] => [3] => [3]
=> 1
[1,0,1,1,0,0]
=> [1,2] => [1,1] => [1,1]
=> 0
[1,1,0,0,1,0]
=> [2,1] => [1,1] => [1,1]
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [4] => [4]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1] => [2,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [1,1,1] => [1,1,1]
=> 0
[1,0,1,1,0,1,0,0]
=> [1,3] => [1,1] => [1,1]
=> 0
[1,0,1,1,1,0,0,0]
=> [1,3] => [1,1] => [1,1]
=> 0
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [1,2] => [2,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2] => [2]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [1,1] => [1,1]
=> 0
[1,1,1,0,0,0,1,0]
=> [3,1] => [1,1] => [1,1]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [5] => [5]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [3,1] => [3,1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1] => [2,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [2,1] => [2,1]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [2,1] => [2,1]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [1,1,2] => [2,1,1]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [1,2] => [2,1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,1,1]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [1,1] => [1,1]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [1,1] => [1,1]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,1,1]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [1,1] => [1,1]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [1,1] => [1,1]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [1,1] => [1,1]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => [3,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => [1,1,1]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1] => [2,1]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [1,1] => [1,1]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [1,1] => [1,1]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [2,1]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,1]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,1]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,1]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [2,1]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,1]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,1]
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,1]
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [1,1] => [1,1]
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [6] => [6]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [4,1] => [4,1]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [3,1,1] => [3,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1] => [3,1]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1] => [3,1]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => [2,2,1]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2] => [2,2]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [2,1,1] => [2,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [2,1] => [2,1]
=> 1
Description
The number of parts of an integer partition that are at least two.
Matching statistic: St001553
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001553: Dyck paths ⟶ ℤResult quality: 75% ●values known / values provided: 93%●distinct values known / distinct values provided: 75%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001553: Dyck paths ⟶ ℤResult quality: 75% ●values known / values provided: 93%●distinct values known / distinct values provided: 75%
Values
[1,0,1,0]
=> [1,1] => [2] => [1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> [1,1,1] => [3] => [1,1,1,0,0,0]
=> 1
[1,0,1,1,0,0]
=> [1,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0]
=> [2,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,0,1,0,0]
=> [1,3] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,0,0]
=> [1,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2] => [1,1,0,0]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,0,1,0]
=> [3,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [1,1,1] => [1,0,1,0,1,0]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [1,2] => [1,0,1,1,0,0]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [1,1] => [1,0,1,0]
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,4] => [2,1] => [1,1,0,0,1,0]
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? = 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,2,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,2,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=> ? = 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,2,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,2,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> ? = 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? = 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? = 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> [1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? = 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> [3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 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] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 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] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 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] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
Description
The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path.
The statistic returns zero in case that bimodule is the zero module.
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